Question

The following observation has been arranged n ascending order :
29, 32, 48, 50, x, x+2, 72, 78, 84, 95.

If the median of the data is 63, then find the value of x.
a. 65
b. 64
c. 63
d. 62.

{AMU +2 ENTRANCE TEST 2013-14}

Answer 1

HELLO DEAR,

TOTAL NUMBER OF OBSERVATIONS = n=10
( ITS EVEN NUMBER)

$median = \frac{ (\frac{n }{2}) ^{th}obse. + ( \frac{n}{2} + 1) ^{th}obsr. }{2} \\ = > 63 = \frac{ (\frac{10}{2})^{th} + (\frac{10}{2} + 1) ^{th} }{2} \\ = > 63 = \frac{5 ^{th}obser. + 6 ^{th} obser. }{2} \\ = > 63 = \frac{x +( x + 2)}{2} \\ = > 63 \times 2 = 2x + 2 \\ = > 126 = 2x + 2 \\ = > 2x = 124 \\ = > x = \frac{124}{2} \\ = > x = 62 \\ \: i \: hope \: its \: help \: you \: dear \: thanks$

Answer 2

Hey Rehan and others .....

There are totally 10 observations i.e n = 10

median = 63

$median \: = \frac{( \frac{n}{2}) ^{th} + ( \frac{n}{2} + 1)^{th} }{2} \\ \\ 63 = \frac{{5}^{th} + {6}^{th} }{2} \\ \\ 63 \times 2 = 2x + 2 \\ \\ 63 = x + 1 \\ \\ x = 62$
Your answer is option (d)


Hope it helps