the following observations have been arranged in ascending order of the median of the data is 23.5 find the value of x the following observations are as follows 12, 16, 17, 19, x, x + 3, 27, 37, 38, 40
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n = 10
Median when no. of terms is even = Mean of (n/2)th and (n/2 + 1)th terms
Median = Mean of 5th and 6th terms
= (x + x + 3)/2
= (2x + 3)/2 --- (1)
Given median = 23.5 --- (2)
Equating (1) and (2)
2x + 3 = 23.5 X 2
2x = 47 - 3
x = 44/2 = 22
Thus x = 22
Median when no. of terms is even = Mean of (n/2)th and (n/2 + 1)th terms
Median = Mean of 5th and 6th terms
= (x + x + 3)/2
= (2x + 3)/2 --- (1)
Given median = 23.5 --- (2)
Equating (1) and (2)
2x + 3 = 23.5 X 2
2x = 47 - 3
x = 44/2 = 22
Thus x = 22
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