# Class 9 RD Sharma Solutions – Chapter 24 Measures of Central Tendency – Exercise 24.3

### Question 1. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 10 (even)

Median =

= 99/2

= 49.5

### Question 2. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 10 (even)

Median =

= 194/2

= 97

### Question 3. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 8 (even)

Median =

= 66/2

= 33

### Question 4. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 9 (odd)

Median =

= 5

^{th}term= 16

### Question 5. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 9 (odd)

Median =

= 5

^{th}term= 71

### Question 6. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 10 (even)

Median =

= 55/2

= 27.5

### Question 7. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 8 (even)

Median =

= 20/2

= 10

### Question 8. Find the median of the following data:

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

**Solution:**

Ascending order sequence of the numbers :

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

Total number of terms, supposedly, n = 10 (even)

Median =

= 136/2

= 68

### 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.

**Solution:**

Ascending order sequence of the numbers :

8, 11, 12, 2x – 8, 2x+10, 35, 42, 50

Total number of terms, supposedly, n = 8 (even)

Given,

Median = 25

Median =

48 = 4x

x = 12

### 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 new data, find the new median?

**Solution:**

Ascending order sequence of the numbers :

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

n = 11 (odd)

Median =

= 6

^{th}term= 58

If we replace 92 by 99 and 41 and 43, then the new sequence of numbers are :

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

New Median =

= 6

^{th}term= 58

### 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?

**Solution: **

Arranging the data given in ascending order :

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

Number of terms, supposedly n = 9 (odd)

Median =

= 5

^{th }term= 61

On replacing the value 58 by 85, we get,

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

New Median =

= 5

^{th }term= 71

### 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 in weight. If the 44 kg is replaced by 446kg and 27 kg by 25kg. Find the new median.

**Solution : **

Arranging the data in ascending order,

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

Total number of terms = 15 (n = odd)

Median =

= 8

^{th}term= 35 kg

On replacing 44 kg by 46 kg and 27 kg by 25 kg respectively, we get,

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

New Median =

= 8

^{th}term= 35 kg

### Question 13. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.

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

**Solution : **

Given,

Median = 63

Total number of terms, supposedly n = 10 (even)

Now,

Median =

63 = x+1

x = 62

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