RD Chapter 24 Measures of Central Tendency Ex 24.3 Solutions
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 n=9 , 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