RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2

RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2

Other Exercises

Question 1.
Explain the reading and interpretation of bar graphs.
Solution:
Reading and interpretation of the bar graph:
The first step in reading a bar graph is to know what it represents or what is the information given by it. For this, we read the captions which are generally written just below the horizontal line (x-axis) and adjacent to vertical line (y-axis). After knowing that what does a bar graph represent we read the scale so that we can know the precise values in the given data.
After reading a bar graph one must be able to draw certain conclusions from it. Drawing some conclusions from a given bar graph means interpretation of the bar graph.

Question 2.
Read the following bar graph and answer the following questions:
(i) What information is given by the bar graph?
(ii) In which year the export is minimum?
(iii) In which year the import is maximum?
(iv) In which year the difference of the values of export and import is maximum?
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 2.1
Solution:
After reading the bar graph. We find:
(i) Export and import in 100 crores of rupees year wise.
(ii) In the year 1982-83, export is minimum i.e. 100 crores.
(iii) In the year 1986-87, import is maximum i.e. 22 hundred crores.
(iv) In the year 1986-87, the difference of the values of import and export is maximum i.e. 22 – 12 = 10 x 100 crore.

Question 3.
The following bar graph show’s the results of an annual examination in a secondary school.
Read the bar graph and choose the correct alternative in each of the following:
(i) The pair of classes in which the results of boys and girls are inversely proportional are:
(a) VI, VIII (b) VI, IX (c) VIII, IX (d) VIII, X
(ii) The class having the lowest failure rate of girls is
(a) VII (b) X (c) IX (d) VIII
(iii) The class having the lowest pass rate of students is
(a) VI (b) VII (c) VIII (d) IX
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 3.1
Solution:
After reading the given bar graph, we find that
(i) The pair of classes in which the results of boys and girls are inversely proportional is VI and IX as in VI, 80% boys and 70% girls and in IX, 70% boys and 80% girls are the results.
(ii) Lowest failure of girls of students is VII as pass % is 100%.
(iii) Class having the lowest pass rate is VII boys as it is 50% only.

Question 4.
The following data gives the number (in thousands) of applicants registered with an Employment Exchange during, 1995-2000:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 4.1
Construct a bar graph to represent the above data.
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 4.2
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 4.3
Bar graph of the above is given below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 4.4

Question 5.
The production of saleable steel in some of the steel plants of our country during 1999 is given below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 5.1
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20 thousands tonnes.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 5.2
Bar graph of the above data is given below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 5.3

Question 6.
The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 6.1
Represent the above data with the help of a bar graph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 6.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 6.3

Question 7.
The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 7.1
(i) Represent the above data with the help of a bar graph.
(ii) With the help of the bar graph, indicate the year in which amount of loan is not increased over that of the preceding year.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 7.2

Question 8.
The following table shows the interest paid by a company (in lakhs):
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 8.1
Draw the bar graph to represent the above information.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 8.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 8.3

Question 9.
The following data shows the average age of men in various countries in a certain year:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 9.1
Represent the above information by a bar graph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 9.2

Question 10.
The following data gives the production of foodgrains (in thousand tonnes) for some years:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 10.1
Represent the above data with the help of a bar graph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 10.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 10.3

Question 11.
The following data gives the amount of manure (in thousand tonnes) manufactured by a company during some years:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 11.1
(i) Represent the above data with the help of a bar graph.
(ii) Indicate with the help of the bar graph the year in which the amount of manufactured by the company was maximum.
(in) Choose the correct alternative:
The consecutive years during which there was maximum decrease in manure production are:
(a) 1994 and 1995
(b) 1992 and 1993
(c) 1996 and 1997
(d) 1995 and 1996
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 11.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 11.3
(ii) The maximum amount of manure manufactured in the year 1994, i.e. 45 thousand tonnes.
(iii) There was maximum decrease in manure production in 1996 and 1997.

Question 12.
The following data gives the demand estimates of the Government of India, Department of Electronics for the personnel in the Computer sector during the Eighth Plan period (1990-95):
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 12.1
Represent the data with the help of a bar graph. Indicate with the help of the bar graph the course where estimated requirement is least.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 12.2
The course where requirement is least is DCE.

Question 13.
The income and expenditure for 5 years of a family is given in the following data:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 13.1
Represent the above data by a bar graph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 13.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 13.3

Question 14.
The investment (in ten crores of rupees) of Life Insurance Corporation of India in different sectors are given below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 14.1
Represent the above data with the help of a bar graph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 14.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 14.3

Question 15.
The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 15.1
Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 15.2

Question 16.
The following table gives the quantity of good (in crore tonnes)
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 16.1
Represent this information with the help of a bar graph.
Explain through the bar graph if the quantity of goods carried by the Indian Railways in 1965-66 is more than double the quantity of goods carried in the year 1950-51.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 16.2

Question 17.
The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 17.1
Construct a bar graph to represent the above data so that the bars are drawn horizontally.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 17.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 17.3

Question 18.
The expenditure (in 10 crores of rupees) on health by the Government of India during the various five year plans is shown below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 18.1
Construct a bar graph to represent the above data.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 18.2

Hope given RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.2 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B

RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 1 Number System Ex 1B.

Other Exercises

Fill in each of the following boxes with the correct symbol > or < :

Question 1.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B 1.1

Question 2.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B 2.1

Question 3.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B 3.1

Question 4.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B 4.1

Question 5.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B 5.1

Question 6.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1B 6.1

Arrange the following numbers in the descending order :

Question 7.
Solution:
102345680 > 63521047 > 63514759 > 7355014 > 7354206

Question 8.
Solution:
23794206 > 23756819 > 5032790 > 5032786 > 987876

Question 9.
Solution:
16060666 > 16007777 > 1808090 > 1808088 > 190909 > 181888

Question 10.
Solution:
1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988.

Arrange the following numbers in the ascending order

Question 11.
Solution:
990357 < 9873426 < 9874012 < 24615019 < 24620010

Question 12.
Solution:
5694437 < 5695440 < 56943201 < 56943300 < 56944000

Question 13.
Solution:
700087 < 8014257 < 8014306 < 8015032 < 10012458

Question 14.
Solution:
893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403

Hope given RS Aggarwal Solutions Class 6 Chapter 1 Number System Ex 1B are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4

RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4

Other Exercises

Question 1.
Find the cube roots of each of the following integers :
(i) -125
(ii) -5832
(iii) -2744000
(iv) -753571
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 1
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 2
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 3
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 4

Question 2.
Show that :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 5
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 6
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 7

Question 3.
Find the cube root of each of the following numbers :
(i) 8 x 125
(ii) -1728 x 216
(iii) -27 x 2744
(iv) -729 x -15625
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 8
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 9

Question 4.
Evaluate :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 10
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 11
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 12

Question 5.
Find the cube root of each of the following rational numbers.
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 13
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 14
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 15
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 16
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 17

Question 6.
Find the cube root of each of the following rational numbers :
(i) 0.001728
(ii) 0.003375
(iii) 0.001
(iv) 1.331
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 18
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 19

Question 7.
Evaluate each of the following :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 20
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 21
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 22
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 23
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 24

Question 8.
Show that :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 25
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 26
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 27
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 28

Question 9.
Fill in the Blanks :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 29
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 30
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 31
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 32
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 33

Question 10.
The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 34
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 35

Question 11.
Three numbers are to one another 2:3: 4. The sum of their cubes is 0.334125. Find the numbers.
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 36
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 37

Question 12.
Find side of a cube whose volume is
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 38
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 39

Question 13.
Evaluate :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 40
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 41
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 42

Question 14.
Find the cube root of the numbers : 2460375,20346417,210644875,57066625 using the fact that
(i) 2460375 = 3375 x 729
(i) 20346417 = 9261 x 2197
(iii) 210644875 = 42875 x 4913
(iv) 57066625 = 166375 x 343
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 43
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 44
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 45

Question 15.
Find the units digit of the cube root of the following numbers ?
(i) 226981
(ii) 13824
(iii) 571787
(iv) 175616
Solution:
(i) 226981
In it unit digit is 1
∴The units digit of its cube root will be = 1
(∵ 1 x 1 x 1 = 1)
∴Tens digit of the cube root will be = 6
(ii) 13824
∵ The units digit of 13824 = 4
(∵ 4 X 4 X 4 = 64)
∴Units digit of the cube root of it = 4
(iii) 571787
∵ The units digit of 571787 is 7
∴The units digit of its cube root = 3
(∵ 3 x 3 x 3 = 27)
(iv) 175616
∵ The units digit of 175616 is 6
∴The units digit of its cube root = 6
(∵ 6 x 6 x 6=216)

Question 16.
Find the tens digit of the cube root of each of the numbers in Question No. 15.
Solution:
(i) In 226981
∵ Units digit is 1
∴Units digit of its cube root = 1
We have 226
(Leaving three digits number 981)
63 = 216 and 73 = 343
∴63 ∠226 ∠ T
∴The ten’s digit of cube root will be 6
(ii) In 13824
Leaving three digits number 824, we have 13
∵ (2)3 = 8, (3)3 = 27
∴23 ∠13 ∠3′
∴Tens digit of cube root will be 2
(iii) In 571787
Leaving three digits number 787, we have 571
83 = 512, 93 = 729
∴ 83 ∠571 ∠93
Tens digit of the cube root will be = 8
(iv) In 175616
Leaving three digit number 616, we have 175
∵ 53 = 125, 63 = 216
∴53 ∠175 ∠63
∴Tens digit of the cube root will be = 5

Hope given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1

RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1

Other Exercises

Question 1.
The following table shows the daily production of T.V. sets in an industry for 7 days of a week:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 1.1
Represent the above information by a pictograph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 1.2
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 1.3
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 1.4

Question 2.
The following table shows the number of Maruti cars sold by five dealers in a particular month:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 2.1
Represent the above information by a pictograph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 2.2

Question 3.
The population of Delhi State in different census years is as given below:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 3.1
Represent the above information with the help of a bar graph.
Solution:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 3.2

Question 4.
Read the bar graph shown in Figure and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 4.1
(i) What is the information given by the bar graph?
(ii) How many tickets of Assam State Lottery were sold by the agent?
(iii) Of which state, were the maximum number of tickets sold?
(iv) State whether true or false.
The maximum number of tickets sold is three times the minimum number of tickets sold.
(v) Of which state were the minimum number of tickets sold?
Solution:
(i) Sale of lottery tickets if different states.
(ii) 40 tickets of Assam state lottery were sold.
(iii) Maximum number of lottery tickets were sold of Haryana state.
(iv) Maximum tickets were 100 and minimum = 20 which are not three time. False.
(v) Minimum Lottery tickets of 10 Rajasthan will sold.

Question 5.
Study the bar graph representing the number of persons in various age groups in a town shown in figure. Observe the bar graph and answer the following questions:
(i) What is the percentage of the youngest age-group persons over those in the oldest age group?
(ii) What is the total population of the town?
(iii) What is the number of persons in the age-group 60-65?
(iv) How many persons are more in the age-group 10-15 than in the age group 30-35?
(v) What is the age-group of exactly 1200 persons living in the town?
(vi) What is the total number of persons living in the town in the age-group 50-55?
(vii) What is the total number of persons living in the town in the age-groups 10-15 and 60-65?
(viii) Whether the population in general increases, decreases or remains constant with the increase in the age-group.
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 5.1
Solution:
(i) Youngest age group = 300 and oldest age group = 1400
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 5.2
(ii) Total population = 1400 + 1200 + 1100 + 1000 + 900 + 800 + 300 – 6700
(iii) In age group of 60-65, number of persons = 800
(iv) Difference of person in the age group 10-15 and of 30-35 = 1400 – 1100 = 300
(v) 1200 persons are in the age group 20-25
(vi) In age group 50-55 number of persons are 900
(vii) Total number of person of the age group 10-15 and
60-65 = 1400 + 800 = 2200
(viii)Population is decreasing with the age-group.

Question 6.
Read the bar graph shown in figure and answer the following questions:
(i) What is the information given by the bar graph?
(ii) What was the number of commercial banks in 1977?
(iii) What is the ratio of the number of commercial banks in 1969 to that in 1980?
(iv) State whether true or false:
The number of commercial banks in 1983 is less than double the number of commercial banks in 1969.
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 6.1
Solution:
(i) The information is number of commercial banks in India during same years.
(ii) In 1977, commercial banks were 130.
(iii) Ratio of banks in 1969 to 1980 = 90 : 150 = 3:5
(iv) Number of banks in 1983 = 230 and number of banks in 1969 = 90
∴ Number of banks in 1983 is less than double the number of banks in 1969 – False.

Question 7.
Given below is the bar graph indicating the marks obtained out of 50 in mathematics paper by 100 students. Read the bar graph and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 7.1
(i) It is decided to distribute work books on mathematics to the students obtaining less than 20 marks, giving one workbook to each of such students. If a work book costs T5, what sum is required to buy the work books?
(ii) Every student belonging to the highest mark group is entitled to get a prize of ? 10. How much amount of money is required for distributing the prize money?
(iii) Every student belonging to the lowest mark-group has to solve 5 problems per day. How many problems, in all, will be solved by the students of this group per day?
(iv) State whether true or false. .
(a) 17% students have obtained marks ranging from 40 to 49.
(b) 59 students have obtained marks ranging from 10 to 29.
(v) What is the number of students getting less than 20 marks?
(vi) What is the number of students getting more than 29 marks?
(vii) What is the number of students getting marks between 9 and 40?
(viii)What is the number of students belonging to the highest mark group?
(ix) What is the number of students obtaining more than 19 marks?
Solution:
(i) Students getting less than 20 marks = 27 + 12 = 39
Cost of 1 work book = ₹5
∴ Total cost = 39 x 5 = ₹195
(ii) No. of students getting highest mark group = 17
∴ Amount paid at the rate of Rs. 10 to each = 10 x 17 = Rs. 170
(iii) Lowest mark group = 27
∴ Total number of problems given = 27 x 5 = 135
(iv) (a) True (b) False
(v) No. of students getting less then 20 marks = 27 + 12 = 39
(vi) Students getting more than 29 marks = 24 + 17 = 41
(vii) Students getting marks between 9 and 40 = 12 + 20 + 24 = 56
(viii) Students to the highest mark group = 17
(ix) Students setting more than 19 marks = 20 + 24 + 17 = 61

Question 8.
Read the following bar graph and answer the following questions:
(i) What is the information given by the bar graph?
(ii) State each of the following whether true or false.
(a) The number of government companies in 1957 is that of 1982 is 1 : 9.
(b) The number of government companies have decreased over the year 1957 to 1983.
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 8.1
Solution:
(i) Number of government companies in India during some years.
(ii) (a) False (b) False
(a) 50 : 400 = 1:8 and (b) companies are increasing not decreasing.

Question 9.
Read the following bar graph and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 9.1
(i) What information is given by the bar graph?
(ii) Which state is the largest producer of rice?
(iii) Which state is the largest producer of wheat?
(iv) Which state has total production of rice and wheat as its maximum?
(v) Which state has the total production of wheat and rice minimum?
Solution:
(i) Production of rice and wheat in different states of India.
(ii) West Bengal is the largest state of production of rice.
(iii) Largest producer of wheat is U.P.
(iv) Maximum production of wheat and rice is U.P.
(v) Minimum production of wheat and rice is Maharashtra.

Question 10.
The following bar graph represents the heights (in cm) of 50 students of Class XI of a particular school. Study the graph and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 10.1
(i) What percentage of the total number of students have their heights more than 149 cm?
(ii) How many students in the class are in the range of maximum height of the class?
(iii) The school wants to provide a particular type of tonic to each student below the height of 150 cm to improve his height. If the cost of the tonic for each student comes out to be Rs. 55, how much amount of money is required?
(iv) How many students are in the range of shortest height of the class?
(v) State whether true or false:
(a) There are 9 students in the class whose heights are in the range of 155-159 cm.
(b) Maximum height (in cm) of a student in the class is 17.
(c) There are 29 students in the class whose heights are in the range of 145-154 cm.
(d) Minimum height (in cm) of a student is the class is in the range of 140-144 cms.
(e) The number of students in the class having their heights less than 150 cm is 12.
(f) There are 14 students each of whom has height more than 154 cm.
Solution:
(i) No. of students having more than height of 149 cm = 17 + 9 + 5 = 31
Percentage = \(\frac { 31 }{ 50 }\) x 100 = 62%
(ii) No. of students in the range of maximum height = 5
(iii) No. of students below the height of 150 cm = 7 + 12 = 19
Cost of tonic for each student = ₹55
∴ Total cost = ₹55 x 19 = ₹1045
(iv) No. of students in the shortest height = 7
(v) (a) True
(b) False
(c) True
(d) True
(e) False
(f) True

Question 11.
Read the following bar graph and answer the following questions:
(i) What information is given by the bar graph?
(ii) What was the production of cement in the year 1980-81?
(iii) What is the minimum and maximum productions of cement and corresponding years?
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 11.1
Solution:
(i) Industrial production of cement in different years in India.
(ii) In the year 1980-81, the production was 186 lakh tonnes.
(iii) Minimum production was 30 lakh tonnes in 1950-51 and maximum production was 232 lakh tonnes in 1982-83.

Question 12.
The bar graph shown in the figure represents the circulation of newspapers in 10 languages. Study the bar graph and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 12.1
(i) What is the total number of newspapers published in Hindi, English, Urdu, Punjabi and Bengali?
(ii) What percent is the number of news papers published in Hindi of the total number of newspapers?
(iii) Find the excess of the number of newspapers published in English over those published in Urdu,
(iv) Name two pairs of languages which publish the same number of newspapers.
(v) State the languages in which the smallest number of newspapers are published.
(vi) State the language in which the largest number of newspapers are published.
(vii) State the language in whih the number of newspapers published is between 2500 and 3500.
(viii)State whether true or false:
(a) The number of newspapers published in Malayalam and Marathi together is- less than those published in English.
(b) The number of newspapers published in Telugu is more than those published in Tamil.
Solution:
(i) Total number of newspapers in Hindi, English, Urdu, Punjabi, and Bengali
= 3700 + 3400 + 700 + 200 + 1100 = 9100
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 12.2
(iii) Difference in English and Urdu = 3400 – 700 = 2700
(iv) Malayalam and Marathi, Bengali and Gujrati
(v) Punjabi (200)
(vi) Hindi (3700)
(vii) English (3400)
(viii)(a) True (b) False

Question 13.
Read the bar graph given in figure and answer the following questions:
(i) What information is given by the bar graph?
(ii) What was the crop-production if rice in 1970-71?
(iii) What is the difference between the maximum and minimum production of rice?
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 13.1
Solution:
(i) Production of rice in India in different years.
(ii) Crop production in 1970-71 was 42.5 lakh tonnes.
(iii) Differences in maximum and minimum production of rice = 55 – 22 lakh tonnes = 33 lakh tonnes

Question 14.
Read the bar graph given in figure and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 14.1
(i) What information does it give?
(ii) in which part the expenditure on education is maximum in 1980?
(iii) In which part the expenditure has gone up from 1980 to 1990?
(iv) In which part the gap between 1980 and 1990 is maximum?
Solution:
(i) Public expenditure on education by vertices sub-continents in 1980 and 1990.
(ii) Maximum expenditure on education in 1980 was in Africa.
(iii) The expenditure from 1980 to 1990 was gone up in East Africa.
(iv) Maximum gap between 1980 and 1990 was in Africa.

Question 15.
Read the bar graph given in the figure and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 15.1
(i) What information is given by the bar graph?
(ii) In whicli years the areas under the sugarcane crop were the maximum and the minimum?
(iii) State whether true or false:
The area under the sugarcane crop in the year 1982-83 is three times that of the year 1950-51.
Solution:
(i) Areas under sugarcane crop during different years in India.
(ii) Maximum sugarcane crop was in 1982-83 and minimum in 1950-51.
(iii) False.

Question 16.
Read the bar graph given in the figure and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 16.1
(i) What information is given by the bar graph?
(ii) What was the expenditure on health and family planning in the year 1982-83?
(iii) In which year is the increase in expenditure maximum over the expenditure in previous year? What is the maximum increase?
Solution:
(i) Expenditure on health and family planning sixth five year plan in India.
(ii) Expenditure during 1982-83 was 700 crore of rupees.
(iii) Maximum increase in 1984-85 was them in previous year and difference 10.2 – 8 = 220 crores.

Question 17.
Read the bar graph given in the figure and answer the following questions:
(i) What is the information given by the bar graph?
(ii) What is the number of families having 6 members?
(iii) How many members per family are there in the maximum number of families? Also tell the number of such families.
(iv) What are the number of members per family for which the number of families are equal? Also, tell the number of such families?
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 17.1
Solution:
(i) Number of families with different number of members in a locality.
(ii) Number of families having 6 members are 50.
(iii) Maximum number of families are of 3 members family and there are 120.
(iv) Number of families having 9 members and having 10 members are equal and each is 5.

Question 18.
Read the bar graph given in the figure and answer the following questions:
RD Sharma Class 9 Solutions Chapter 23 Graphical Representation of Statistical Data Ex 23.1 18.1
(i) What information is given by the bar graph?
(ii) Which Doordarshan centre covers maximum area? Also tell the covered area.
(iii) What is the difference between the areas covered by the centres at Delhi and Bombay?
(iv) Which Doordarshan centres are in U.P. State? What are the areas covered by them?
Solution:
(i) Coverage of some Doordarshan centres of India.
(ii) Doordarshan kender Kolkata covers maximum area which is 36000 sq. km.
(iii) Difference of areas covered by Delhi and Bombay centres = 32000 – 18000 = 14000 sq. km.
(iv) In U.R Doordarshan centres are Kanpur (32000 sq. km) and Lucknow (25000 sq. km).

 

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RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1A

RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1A

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 1 Number System Ex 1A

Other Exercises

Question 1.
Solution:
(i) Nine thousand eighteen = 9,018.
(ii) Fifty four thousand seventy three = 54,073
(iii) Three lakh two thousand five hundred six = 3,02,506.
(iv) Twenty lakh ten thousand eight = 20,10,008.
(v) Six crore five lakh fifty-seven = 6,05,00,057.
(vi) Two crore two lakh two thousand two hundred two = 2,02,02,202.
(vii) Twelve crore twelve lakh twelve thousand twelve = 12,12,12,012.
(viii) Fifteen crore fifty lakh twenty thousand sixty-eight = 15,50,20,068.

Question 2.
Solution:
(i) 63,005 = Sixty three thousand five.
(ii)7,07,075 = Seven lakh, seven thousand seventy five.
(iii) 34,20,019 = Thirty-four lakh twenty thousand nineteen.
(iv) 3,05,09,0.12 = Three crore, five lakh, nine thousand twelve.
(v) 5,10,03,604 = Five crore ten lakh three thousand six hundred four.
(vi) 6,18,05,008 = Six crore eighteen lakh five thousand eight.
(vii) 19,09,09,900 = Nineteen crore nine lakh, nine thousand nine hundred.
(viii) 6,15.30,807 = Six crore fifteen lakh, thirty thousand eight hundred seven.
(ix) 6,60,60,060 = Six crore sixty lakh sixty thousand sixty. Ans.

Question 3.
Solution:
(i) 15,768 = (1 x 10000) + (5 x 1000) + (7 x 100) + (6 x 10) + (8 x 1)
(ii) 3,08,927 = (3 x 100000) + (8 x 1000) + (9 x 100) +(2 x 10) +(7 x 1)
(iii) 24,05,609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) + (9 x 1)
(iv) 5,36,18,493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000) + (1 x 10000) + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)
(v) 6,06,06,006 = (6 x 10000000) + (6 x 100000) + (6 x 1000) + (6 x 1)
(vi) 9,10,10,510 = (9 x 10000000) + (1 x 1000000) + (1 x 10000) + (5 x 100) + (1 x 10) Ans,

Question 4.
Solution:
(i) 6 x 10000 + 2 x 1000 + 5 x 100 + 8 x 10 + 4 x 1
= 60000 + 2000 + 500 + 80 + 4
= 62,584.
(ii) 5 x 100000 + 8 x 10000 + 1 x 1000 + 6 x 100 + 2 x 10 + 3 x 1
= 500000 + 80000 + 1000 + 600 + 20 + 3
= 5,81,623
(iii) 2 x 10000000 + 5 x 100000 + 7 x 1000 + 9 x 100 + 5 x 1
= 20000000 + 500000 + 7000 + 900 + 5
= 2,05,07,905
(iv) 3 x 1000000 + 4 x 100000 + 6 x 1000 + 5 x 100 + 7 x 1
= 3000000 + 400000 + 6000 + 500 + 7
= 34,06,507 Ans.

Question 5.
Solution:
In 79520986
Value of first 9 = 9000000
and value of second 9 = 900
Difference = 9000000 – 900
= 89,99,100 Ans.

Question 6.
Solution:
In 27650934
place value of 7 = 7000000
and face value of 7 = 7
Difference = 7000000 – 7
= 6999993 Ans.

Question 7.
Solution:
There are 900000 6-digits numbers in all
i.e. 999999 – 99999
= 900000 Ans

Question 8.
Solution:
There are 9999999 – 999999
= 9000000 7-digits numbers in all.

Question 9.
Solution:
In 1,00,000, there are 100 thousands. Ans.

Question 10.
Solution:
In 10000,000, there are 10000 thousands.

Question 11.
Solution:
Given Number = 738
Reversing its digits = 837
Difference between 738 and 837
= 837 – 738
= 99 Ans.

Question 12.
Solution:
Numbers after 9547999
= 9547999 + 1
= 9548000 Ans.

Question 13.
Solution:
Number first before 9900000
= 9900000 – 1
= 9899999 Ans.

Question 14.
Solution:
Number first before 10000000
= 10000000 – 1
= 9999999 Ans.

Question 15.
Solution:
3-digits numbers using 2, 3, 4 taking each digit only once will be
234, 243, 324, 342, 423, 432 Ans.

Question 16.
Solution:
The smallest number by using different digits 3, 1, 0, 5 and 7 will be
= 10357 Ans.

Question 17.
Solution:
The largest number formed by using different digits 2, 4, 0, 3, 6 and 9 will be
= 964320. Ans.

Question 18.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1A 18.1
(i) Seven hundred thirty five thousand eight hundred twenty-one.
(ii) Six million fifty seven thousand eight hundred ninety-four.
(iii) Fifty-six million nine hundred forty-three thousand eight hundred twenty-one.
(iv) Thirty-seven million five hundred two thousand ninety-three.
(v) Eighty-nine million three hundred fifty thousand sixty-four.
(vi) Ninety million seven hundred three thousand and six. Ans.

Question 19.
Solution:
RS Aggarwal Class 6 Solutions Chapter 1 Number System Ex 1A 19.1

OBJECTIVE QUESTIONS
Tick the correct answer in each of the following :

Question 20.
Solution:
(c) Because 6 is at lakh place.

Question 21.
Solution:
(a) Because face value is always same.

Question 22.
Solution:
(b) Because place value and face value of 5 in 87653421 are 50000 and 5.
difference
= 50000 – 5
= 49995.

Question 23.
Solution:
(b) Smallest counting number or natural number is 1.

Question 24.
Solution:
(b) Number of 4-digits numbers
= 9999 – 999 (i.e. these are 1000 to 9999)
= 9000

Question 25.
Solution:
(b) Number of 7-digit numbers (from 1000000 to 9999999)
= 9999999 – 999999
= 9000000

Question 26.
Solution:
(c) Numbers of 8-digit numbers (from 10000000 to 99999999)
= 99999999 – 9999999
= 90000000

Question 27.
Solution:
(b) Because 1000000 – 1
= 999999 Ans.

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RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25C

RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25C

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 25 Graphs Ex 25C.

Other Exercises

OBJECTIVE QUESTIONS
Tick the correct answer in each of the following:

Question 1.
Solution:
Answer = (a)
∵ In point (3, 6), both x and y are positive.

Question 2.
Solution:
Answer = (c)
∵ In point ( – 7, – 1) both x and y are negative.

Question 3.
Solution:
Answer = (d)
∵ In point (2, – 3), x is positive and y is negative.

Question 4.
Solution:
Answer = (b)
∵ In point ( – 4, 1), x is negative and y is positive.

Question 5.
Solution:
Answer = (c)
∵ Abscissa is distance of a point from y- axis

Question 6.
Solution:
Answer = (d)
y = a is a line parallel to x-axis at a distance of ‘a’ units.

Question 7.
Solution:
Answer = (a)
The equation of the line y-axis, is x = 0

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RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B

RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 25 Graphs Ex 25B.

Other Exercises

Question 1.
Solution:
(a) y = 3x
By giving some different values to x, we shall get corresponding values of y.
x = 1 then y = 3 x 1 = 3
if x = 2, then y = 3 x 2 = 6
if x = 0, then y = 3 x 0 = 0
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B 1.1
Now plotting the points given above, and joining them.
(b) We get a line, From the graph.
(i) When x = 3, then y = 9
(ii) When x = 5, then y = 15
(iii) When x = 6, then y = 18 Ans.
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B 1.2

Question 2.
Solution:
(a) P = 4x
By giving some different values to x, we get the corresponding values of y or P
If x = 1, then P = 4 x 1 = 4
if x = 2, then P = 4 x 2 = 8
if x = 0, then P = 4 x 0 = 0
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B 2.1
Plot the points (1, 4), (2, 8) and 0, 0) on the graph and join then to get the graph of P = 4x as shown
(b) From the graph we see that
(i) When x = 3, then P = 12
(ii) When x = 4, then P = 16
(iii) When x = 6, then P = 24 Ans.
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B 2.2

Question 3.
Solution:
A = x²
giving some values to x, we get corresponding values of y or A
If x = 1, then y or A = (1)² = 1
If x = 2, then y or A = (2)² = 4
If x = 0, then y or A = (0)² = 0
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B 3.1
Now plot the point (1, 1), (2, 4), (0, 0) on the graph, and join them to get the graph of A = x2 as shown
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25B 3.2
(b) From the graph we see that
(i) When x = 2, then A = 4
(ii) When x = 3, then A = 9
(ii) When x = 4 then A = 16 Ans.

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RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25A

RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25A

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 25 Graphs Ex 25A.

Other Exercises

Question 1.
Solution:
Below is given the graph in which X’OX and YOY’ are the co-ordinate axes intersecting each other at O. Now the. points given have been plotted as shown on the graph.
RS Aggarwal Class 8 Solutions Chapter 25 Graphs Ex 25A 1.1

 

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RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data MCQS

RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data MCQS

Other Exercises

Mark the correct alternative in each of the following:
Question 1.
Tally marks are used to find
(a) class intervals
(b) range
(c) frequency
(d) upper limits
Solution:
Frequency (c)

Question 2.
The difference between the highest and lowest values of the observations is called
(a) frequency
(b) mean
(c) range
(d) class intervals
Solution:
range (c)

Question 3.
The difference between the upper limit and the lower class limits is called
(a) mid-points
(b) class size
(c) frequency
(d) mean
Solution:
class size (b)

Question 4.
In the class intervals 10-20, 20-30, 20 is taken in
(a) the interval 10-20
(b) the interval 20-30
(c) both interval 10-20, 20-30
(d) none of the intervals
Solution:
the interval 20-30 (b)

Question 5.
In a frequency distribution, the mid value of a class is 15 and the class intervals is 4. The lower limit of the class is
(a) 10
(b) 12
(c) 13
(d) 14
Solution:
Mid value = 15 and class interval is 4
∴ Lower limit = 15 – \(\frac { 4 }{ 5 }\) = 15 – 2 = 13 (c)

Question 6.
The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are
(a) 47 and 37
(b) 37 and 47
(c) 37.5 and 47.5
(d) 47.5 and 37.5
Solution:
Mid value = 42 and class size =10
∴ Upper limit = 42 + \(\frac { 10 }{ 2 }\) = 42 + 5 = 47
and lower limit = 42 – \(\frac { 10 }{ 2 }\) = 42 – 5 = 37
Upper class limit and lower class limits are 47, 37 (a)

Question 7.
The number of times a particular item occurs in a given data is called its
(a) variation
(b) frequency
(c) cumulative frequency
(d) class-size
Solution:
frequency (b)

Question 8.
The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is
(a) 35.6
(b) 33.1
(c) 30.6
(d) 28.1
Solution:
Width of each class = 2.5
No. of classes = 9
Lower class boundary of the lowest class = 10.6
∴ Upper class limit of highest class = 10.6 + 9 x 2.5
= 10.6 + 22.5 = 33.1 (b)

Question 9.
The following marks were obtained by the students in a test:
81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62
The range of the marks is
(a) 9
(b) 17
(c) 27
(d) 33
Solution:
Marks are 81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62
Here highest marks = 95
and lowest marks = 62
∴ Range = highest marks – lowest marks = 95 – 62 = 33 (d)

Question 10.
Tallys are usually marked in a bunch of
(a) 3
(b) 4
(c) 5
(d) 6
Solution:
4 i.e. IIII (b)

Question 11.
Let l be the lower class limit of a class- interval in a frequency distribution and m be the mid-point of the class. Then, the upper class limit of the class is
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data MCQS 11.1
Solution:
l is the lower class limit of a class interval
m is the mid point of the class
m = \(\frac { u+l }{ 2 }\)
⇒ 2m = u+ l ⇒ u = 2m – l
Then, upper class limit = 2 m – l (c)

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RS Aggarwal Class 8 Solutions Chapter 24 Probability Ex 24B

RS Aggarwal Class 8 Solutions Chapter 24 Probability Ex 24B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 24 Probability Ex 24B.

Other Exercises

Tick the correct answer in each of the following :

Question 1.
Solution:
A spinning wheel has 3 white and 5 green sectors
Possible out come = 3 + 5 = 8
It is spinners, then
Probability of getting a green sector = \(\\ \frac { 5 }{ 8 } \) (b)

Question 2.
Solution:
8 cards are numbered 1, 2, 3, 4, 5, 6, 7, 8
They are mixed and kept in a box One card is chosen at random, then Probability of card having 9 number less than 4 = \(\\ \frac { 3 }{ 8 } \) (c)

Question 3.
Solution:
Two coins are tossed simultaneously, then Possible outcomes = 4
Now probability of getting one head and one tail = \(\\ \frac { 2 }{ 4 } \) = \(\\ \frac { 1 }{ 2 } \) (b)

Question 4.
Solution:
. In a bag, there are 3 white and 2 red balls
Possible outcomes = 3 + 2 = 5
Now probability of a red ball drawn
= \(\\ \frac { 2 }{ 5 } \) (d)

Question 5.
Solution:
A die is thrown then
Possible outcomes = 6
Now probability of getting 6 is \(\\ \frac { 1 }{ 6 } \) (b)

Question 6.
Solution:
A die is thrown
Possible outcomes = 6
Now probability of getting an even number
which are 2, 4, 6 = \(\\ \frac { 3 }{ 6 } \) = \(\\ \frac { 1 }{ 2 } \) (a)

Question 7.
Solution:
One card is drawn from a well shuffled deck of 52 cards, possible out comes = 52
The probability of card which is a queen = \(\\ \frac { 4 }{ 52 } \)
= \(\\ \frac { 1 }{ 13 } \) (c)

Question 8.
Solution:
One card is drawn from a well-shuffled deck of 52 card, possible out comes = 52 Probability of a card being a black 6
(which are two) = \(\\ \frac { 2 }{ 52 } \) = \(\\ \frac { 1 }{ 26 } \) (b)

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RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2

RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2

Other Exercises

Question 1.
Define cumulative frequency distribution.
Solution:
Cumulative frequency : In a discrete frequency distribution, the cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.

Question 2.
Explain the difference between a frequency distribution and a cumulative frequency distribution.
Solution:
The number of times an observation occurs in the given data, is called frequency of the
observation while a cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.

Question 3.
The marks scored by 55 students in a test are given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 3.1
Prepare a cumulative frequency table.
Solution:
Cumulative frequency table is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 3.2

Question 4.
Following are the ages of 360 patients getting medical treatment in a hospital on a day:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 4.1
Construct a cumulative frequency distribution.
Solution:
Cumulative frequency distribution table (less than) is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 4.2

Question 5.
The water bills (in rupees) of 32 houses in a certain street for the period 1.1.98 to 31.3.98 are given below:
56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59.
Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals.
Solution:
Highest bill = 95 Lowest bill = 24
Range = 95 – 24 = 71
Cumulative frequency table is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 5.1

Question 6.
The number of books in different shelves of a library are as follows:
30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20, 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34,
38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25, 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23,
43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.
Prepare a cumulative frequency distribution table using 45-49 as the last class interval.
Solution:
Greatest number = 43
Lowest number =16
Range = 43 – 16 = 27
Cumulative frequency table is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 6.1

Question 7.
Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 7.1
Solution:
The frequency table of the given cumulative frequency is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 7.2

Question 8.
The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 8.1
(i) Represent this as a frequency distribution table.
(ii) Prepare a cumulative frequency table.
Solution:
(i) The frequency distribution table is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 8.2
(ii) Now cumulative frequency table (more then)
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 8.3

Question 9.
Given below is a cumulative frequency distribution table showing the ages of people living in a locality.
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 9.1
Prepare a frequency distribution table.
Solution:
Frequency distribution table is given below:
RD Sharma Class 9 Solutions Chapter 22 Tabular Representation of Statistical Data Ex 22.2 9.2

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