If the median of the observations 19, 21, 23, 35, 37, x, x+2, 71, 79, 80, 92, 95 arranged in ascending order is 50. Find the value of ‘x’.

# If the median of the observations 19, 21, 23, 35, 37, x, x+2, 71, 79, 80, 92, 95 arranged in ascending order is 50. Find the value of ‘x’.

1. A

49

2. B

48

3. C

51

4. D

53

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### Solution:

19, 21, 23, 35, 37, x, x+2, 71, 79, 80, 92, 95

Number of observations are $n=2$

$\therefore$ median is Average of  $\frac{{n}^{th}}{2},{\left(\frac{n}{2}+1\right)}^{th}$ terms

Median is Average of   $\frac{{12}^{th}}{2},{\left(\frac{12}{6}+1\right)}^{th}$  terms

Median is Average of ${6}^{th},{7}^{th}$

Median $=$  average of ${6}^{th},{7}^{th}$  terns is $=\frac{n+n+2}{2}=50$

$⇒2n+2=100$

$⇒x=49$

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