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Question

Ten observations 6, 14, 15, 17, x+1, 2x – 13, 30, 32, 34 and 43 are written in an ascending order. The median of the data is 24. Find the value of x.

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Solution

Given observations are 6, 14, 15, 17, x+1, 2x - 13, 30, 32, 34, 43
Here, total number of observations, n = 10 (even)
Since, n is even, so we use the formula for median,
Median =(n2)th observation+(n2+1)th observation2=(102)th observation+(102+1)th observation2
=5th observation+6th observation2
24=(x+1)+(2x13)2 [given]
3x12=483x=60x=20
Hence, the value of x is 20.

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