Question

If the median of the observations $4,6,7,x,x+2,12,12,13$ arranged in an increasing order is 9,then the variance of these observations is

• A. $\dfrac{37}{4}$
• B. $\dfrac{38}{4}$
• C. $8$
• D. $9$
• E. $10$

Answer 1

Answer: (A)

$\dfrac{37}{4}$

Answer 2

Give data

$4,6,7,x,x+2,12,12,13$

and mean($x̄$) $=9$

Then as there are 8 observations , so

$\dfrac{x+x+2}{2}=9$

$⇒x=8$

$x_i$	$(x_i-x̄)$	$(x_i-x̄)^{2}$
4	-5	25
6	-3	9
7	-2	4
8	-1	1
10	1	1
12	3	9
12	3	9
13	4	16
	74

Therefore, the two terms are $8 , (8+2=)10$ respectively.

Now, Then Variance($σ^2$)$=\dfrac{1}{8}×74= \dfrac{37}{4}$ (_Ans.)