Question

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

Answer 1

ANSWER:
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 n/2th term and n/2+1th term
⇒65=mean of 10/2th term and 10/2+1th term
⇒65=mean of 5th term and 6th term
⇒65=mean of x and x+2
⇒65=(x+x+2)2⇒65×2=2x+2⇒130=2x+2⇒2x=130-2⇒2x=128⇒x=64
Hence, the value of x is 64.