RD Sharma 2020 solution class 9 chapter 24 Measures of Central Tendency Exercise 24.3

Exercise 24.3

Page-24.17

Question 1:

Find the median of the following data (1-8)

83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Answer 1:

The given data is 83, 37, 70, 29, 45, 63, 41, 70, 34 and 54.

Arranging the given data in ascending order, we have

29, 34, 37, 41, 45, 54, 63, 70, 70, 83

Here, the number of observation, which is an even number.

Hence, the median is

Question 2:

133, 73, 89, 108, 94, 104, 94, 85, 100, 120

Answer 2:

The given data is 133, 73, 89, 108, 94, 104, 94, 85, 100 and 120.

Arranging the given data in ascending order, we have

73, 85, 89, 94, 94, 100, 104, 108, 120, 133

Here, the number of observation, which is an even number.

Hence, the median is

Question 3:

31, 38, 27, 28, 36, 25, 35, 40

Answer 3:

The given data is 31, 38, 27, 28, 36, 25, 35 and 40.

Arranging the given data in ascending order, we have

25, 27, 28, 31, 35, 36, 38, 40

Here, the number of observation, which is an even number.

Hence, the median is

Question 4:

15, 6, 16, 8, 22, 21, 9, 18, 25

Answer 4:

The given data is 15, 6, 16, 8, 22, 21, 9, 18, and 25.

Arranging the given data in ascending order, we have

6, 8, 9, 15, 16, 18, 21, 22, 25

Here, the number of observation, which is an odd number.

Hence, the median is

Question 5:

41, 43, 127, 99, 71, 92, 71, 58, 57

Answer 5:

The given data is 41, 43, 127, 99, 71, 92, 71, 58 and 57.

Arranging the given data in ascending order, we have

41, 43, 57, 58, 71, 71, 92, 99, 127

Here, the number of observation, which is an odd number.

Hence, the median is

Question 6:

25, 34, 31, 23, 22, 26, 35, 29, 20, 32

Answer 6:

The given data is 25, 34, 31, 23, 22, 26, 35, 29, 20 and 32.

Arranging the given data in ascending order, we have

20, 22, 23, 25, 26, 29, 31, 32, 34, 35

Here, the number of observation, which is an even number.

Hence, the median is

Question 7:

12, 17, 3, 14, 5, 8, 7, 15

Answer 7:

The given data is 12, 17, 3, 14, 5, 8, 7 and 15.

Arranging the given data in ascending order, we have

3, 5, 7, 8, 12, 14, 15, 17

Here, the number of observation, which is an even number.

Hence, the median is

Question 8:

92, 35, 67, 85, 72, 81, 56, 51, 42, 69

Answer 8:

The given data is 92, 35, 67, 85, 72, 81, 56, 51, 42 and 69.

Arranging the given data in ascending order, we have

35, 42, 51, 56, 67, 69, 72, 81, 85, 92

Here, the number of observation, which is an even number.

Hence, the median is

Question 9:

Numbers 50, 42, 35, 2x + 10, 2x − 8, 12, 11, 8 are written in descending order and their median is 25, find x.

Answer 9:

The given data in descending order is

50, 42, 35, 2x+10, 2x-8, 12, 11, 8

Here, the number of observation, which is an even number.

Hence, the median is

But, it is given that the median is 25. Hence, we have

Question 10:

Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

Answer 10:

The given data is 46, 64, 87, 41, 58, 77, 35, 90, 55, 92 and 33.

Arranging the given data in ascending order, we have

33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

Here, the number of observation, which is an odd number.

Hence, the median is

If 92 and 41 are replaced by 99 and 43 respectively, then the given data becomes 46, 64, 87, 43, 58, 77, 35, 90, 55, 99 and 33.

Arranging the new data in ascending order, we have

33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99

Here, the number of observation, which is an odd number.

Hence, the new median is

Question 11:

Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57 If 58 is replaced by 85, what will be the new median

Answer 11:

The given data is 41, 43, 127, 99, 61, 92, 71, 58 and 57.

Arranging the given data in ascending order, we have

41, 43, 57, 58, 61, 71, 92, 99, 127

Here, the number of observation, which is an odd number.

Hence, the median is

Ifis replaced by 85, then the given data become 41, 43, 127, 99, 61, 92, 71, 85 and 57.

Arranging the new data in ascending order, we have

41, 43, 57, 61, 71, 85, 92, 99, 127

Here, the number of observation, which is an odd number.

Hence, the new median is

Question 12:

The weights (in kg) of 15 students are : 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.

Answer 12:

The weights (in kg) of 15 students are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42 and 30.

Arranging them in ascending order, we have

27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45

Here, the number of observation, which is an odd number.

Hence, the median is

If the weights 44kg and 27kg are replaced by 46kg and 25kg respectively, then the given data becomes 31, 35, 25, 29, 32, 43, 37, 41, 34, 28, 36, 46, 45, 42 and 30.

Arranging the new data in ascending order, we have

25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46

Here, the number of observation, which is an odd number.

Hence, the new median is

Question 13:

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x:

23, 32, 48, 50, x, x+2, 72, 78, 84, 95

Answer 13:

The given data in ascending order is

29, 32, 48, 50, x, x+2, 72, 78, 84, 95

Here, the number of observation, which is an even number.

Hence, the median is

But, it is given that the median is 63. Hence, we have