RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Test Yourself

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Test Yourself.

Other Exercises

Question 1.
Solution:
Correct option: (b)
The cumulative frequency table is useful in determining the median.

Question 2.
Solution:
Correct option: (c)
Mean = 27
Median = 33
Mode = 3Median – 2Mean
= 3 x 33 – 2 x 27
= 99 – 54
= 45

Question 3.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 1

Question 4.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 2

Question 5.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 3

Question 6.
Solution:
Number of athletes who completed the race in less than 14.6 seconds
= 2 + 4 + 15 + 54
= 75.

Question 7.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 4

Question 8.
Solution:
The frequency table is as follows:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 5
The frequency corresponding to the class 20 – 25 is 4.

Question 9.
Solution:

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 6

Question 10.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 7

Question 11.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 8

Question 12.
Solution:

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 9

Question 13.
Solution:
We plot the points (10, 3), (20, 11), (30, 28), (40, 48) and (50, 70) to get the cumulative frequency curve as follows:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 10

Question 14.
Solution:

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 11

Question 15.
Solution:
We plot the points (20, 2), (30, 7), (40, 17), (50, 40), (60, 60), (70, 82), (80, 85), (90, 90) and (100, 100) to get the cumulative frequency curve as follows:

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 12
Here, N = 100 ⇒ N/2 = 50
At y = 50, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 56.
Hence, median = 56

Question 16.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 13

Question 17.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 14

Question 18.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 15

Question 19.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 16

Question 20.
Solution:
Less Than Series:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 17

We plot the points (10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27) and (40, 30) to get less than ogive.

More Than Series:

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 18
We plot the points (5, 30), (10, 28), (15, 16), (20, 14), (25, 10), (30, 7) and (35, 3) to get more than ogive.

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 19

The two curves intersect at L. Draw LM ⊥ OX.

Thus, median = OM = 16.

Question 21.
Solution:
Less Than Series:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 20

We plot the points (45, 1), (50, 10), (55, 25), (60, 43), (65, 83), (35, 27), (70, 109), (75, 125), (80, 139) and (85, 149) to get less than ogive.

More Than Series:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 21

We plot the points (40, 149), (45, 148), (50, 139), (55, 124), (60, 106), (65, 66), (70, 40), (75, 24) and (80, 10) to get more than ogive.

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 22

Question 22.
Solution:
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself 23

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