10,11,13,14,x,17,18,19,21,23
if median is 16, then find value of x

Dear Student,

Given observations: 10, 11, 13, 14, x, 17, 18, 19, 21, 23There are 10 observations in all (n = no. of observations = 10) and the median is 16.Since, the number of observations is even, the median is the mean of the n2th and n2 + 1th observations.Now, n2th observation = 102th observation = 5th observation = x; and n2 + 1th observation = 102 + 1th observation = 6th observation = 17. Median = 16 = 5th observation + 6th observation2 16 = x + 172 32 = x + 17 x = 32 - 17 x = 15NOTE: It is assumed here that all the given observations are arranged in ascending order.

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x-17/2=16
x-17=16 *2
x-17=32
x=32-17
x=15
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