Chapter 24 Measure of Central Tendency R.D. Sharma Solutions for Class 9th Exercise 24.3
Exercise 24.31. Find the median of the following data (1-8)
83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Solution
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 n = 10 , which is an even number.
Hence, the median is
2. 133, 73, 89, 108, 94, 104, 94, 85, 100, 120
Solution
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 n = 10 , which is an even number.
Hence, the median is
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 n = 10 , which is an even number.
Hence, the median is
2. 133, 73, 89, 108, 94, 104, 94, 85, 100, 120
Solution
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 n = 10 , which is an even number.
Hence, the median is
3. 31, 38, 27, 28, 36, 25, 35, 40
Solution
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 n = 10, which is an even number.
Hence, the median is
4. 15, 6, 16, 8, 22, 21, 9, 18, 25
Solution
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 n = 9, which is an odd number.
Hence, the median is
5. 41, 43, 127, 99, 71, 92, 71, 58, 57
Solution
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 n = 9, which is an odd number.
Hence, the median is
6. 25, 34, 31, 23, 22, 26, 35, 29, 20, 32
Solution
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 n = 10, which is an even number.
Hence, the median is
7. 12, 17, 3, 14, 5, 8, 7, 15
Solution
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 n = 8 , which is an even number.
Hence, the median is
8. 92, 35, 67, 85, 72, 81, 56, 51, 42, 69
Solution
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 n = 10, which is an even number.
Hence, the median is
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
The given data in descending order is
50, 42, 35, 2x+10, 2x-8, 12, 11, 8
Here, the number of observation n = 8, which is an even number.
Hence, the median is
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 ?
Solution
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 n = 11, 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 n = 11, which is an odd number.
Hence, the new median is
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
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 n = 9 , which is an odd number.
Hence, the median is
If 58 is 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 n = 9, which is an odd number.
Hence, the new median is
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.
Solution
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 n = 15, 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 n = 15, which is an odd number.
Hence, the new median is
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
Solution
The given data in ascending order is
29, 32, 48, 50, x, x+2, 72, 78, 84, 95
Here, the number of observation n = 10, which is an even number.
Hence, the median is
Here, the number of observation n = 10, which is an even number.
Hence, the median is