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Question

The following observations are arranged in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.
If the median is 65, find the value of x.

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Solution

Arranging the given data in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93

Number of terms = 10 (even)

Median=mean of n2th term and n2+1th term65=mean of 102th term and 102+1th term65=mean of 5th term and 6th term65=mean of x and x+265=x+x+2265×2=2x+2130=2x+22x=130-22x=128x=64

Hence, the value of x is 64.

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