RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5

Other Exercises

Question 1.
Find the mode of the following data :
(i) 3, 5, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
(ii) 3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
(iii) 15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 1
We see that 5 occurs in maximum times which is 5
∴ Mode = 5
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 2
we see that 3 occurs in maximum times i.e. 5
∴ Mode = 3
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 3
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 4
Here we see that 15 occurs in maximum times i.e. 54
∴ Mode = 15

Question 2.
The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows :
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 5
Find the model shirt size worn by the group.
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 6
We see that frequency of 40 is maximum which is 41
∴Mode = 40

Question 3.
Find the mode of the following distribution.
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 7
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 8
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 9
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 10
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 11

Question 4.
Compare the modal ages of two groups of students appearing for an entrance test :
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 12
Solution:
(i) For group A
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 13
We see that class 18-20 has the maximum frequency
∴ It is a modal class
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 14

(ii)  For group B
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 15
We see that class 18-20 has the maximum frequency
∴ It is a modal class
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 16
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 17

Question 5.
The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 18
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 19
We see that class 50-60 has the maximum frequency 20
∴ It is a modal class
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 20

Question 6.
The following is the distribution of height of students of a certain class in a certain city :
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 21
Find the average height of maximum number of students.
Solution:
Writing the classes in exclusive form,
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 22
Here model class is 165.5 – 168.5
and l = 165.5, h = 3, f= 142, f1= 118, f2= 127
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 23
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 24

Question 7.
The following table shows the ages of the patients admitted in a hospital during a year :
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 25
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 26
(i) We see that class 35-45 has the maximum frequency 23
∴ It is a modal class
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 27
= 35.375 = 35.37 years
We see that mean is less than its mode

Question 8.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 28
Determine the modal lifetimes of the components.
Solution:

RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 29
We see that class 60-80 has the maximum frequency 61
∴ It is the modal class
Here l = 60, f= 6, f1 = 52, f2 = 38,h = 20
∴ Modal of life time (in hrs.)
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 30

Question 9.
The following table gives the daily income of 50 workers of a factory :
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 31
Find the mean, mode and median of the above data. (C.B.S.E. 2009)
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 32
Here i = 20 and AM = 150
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 33
(ii) Max frequency  = 14
∴ Model class = 120 – 140
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 34

Question 10.
The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret, the two measures:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 35
Solution:
Let assumed mean (A) = 32.5
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 36
(i)  We see that the class 30-35 has the maximum frequency
∴ It is the modal class
Here l = 30,f = 10, f1 = 9, f2 = 3, h = 5
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 37

Question 11.
Find the mean, median and mode of the following data:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 38
Solution:
Let assumed mean (A) =175
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 39
(i) Here N = 25, \(\frac { 5 }{ 3 }\) = \(\frac { 25 }{ 2 }\) = 12.5 or 13 which lies in the class 150-200
l= 150, F= 10, f= 6, h = 50
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 40
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 41

Question 12.
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data.
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 42
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 43
We see that class 40-50 has the maximum frequency
∴ It is a modal class
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 44

Question 13.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 45
Solution:
Let assumed mean (A) = 135
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 46
Here N = 68 , \(\frac { N }{ 2 }\) = \(\frac { 68 }{ 2 }\) = 34
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 47

Question 14.
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 48
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, And the modal size of the surnames.
Solution:
Let Assumed mean (A) = 8.5
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 49
(i) Here N = 100, \(\frac { N }{ 2 }\) = \(\frac { 100 }{ 2 }\) = 50 which lies in the class 7-10
Here l = 7, F = 36, f= 40, h = 3
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 50

Question 15.
Find the mean, median and mode of the following data (C.B.S.E. 2008)
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 51
Solution:
Let assumed mean A = 70
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 52
(i) Here N = 50, then \(\frac { N }{ 2 }\) = \(\frac { 50 }{ 2 }\) = 25 which lies in the class 60-80
∴ l= 60, F= 24, f = 12 , h = 20
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 53

Question 16.
The following data gives the distribution of total monthly household expenditure of 200 families of a village. .Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 54
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 55
(i) We see that the c ass 1500-2000 has maximum frequency 40
∴ It is a modal class
Here l = 1500, f = 40 , f1 = 24 , f2 = 33 , h =500
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 56

Question 17.
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 57
Find the mode of the data.
Solution:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 58
We see that class 4000-5000 has the maximum frequency 18
∴It is a modal class
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 59

Question 18.
The frequency distribution table of agriculture holdings in a village is given below:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 60
Find the modal agriculture holdings of the village.
Solution:
Here the maximum class frequency is 80,
and the class corresponding to this frequency is 5-7.
So, the modal class is 5-7.
l (lower limit of modal class) = 5
f1 (frequency of the modal class) = 80
f0 (frequency of the class preceding the modal class) = 45
f2(frequency of the class succeeding the modal class) = 55
h (class size) = 2
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 61
Hence, the modal agricultural holdings of the village is 6.2 hectares.

Question 19.
The monthly income of 100 families are given as below:
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 62
Solution:
In a given data, the highest frequency is 41, which lies in the interval 10000-15000.
Here, l = 10000,f1 = 41, f0 = 26,f2 = 16 and h = 5000
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.5 63

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