Question

Find the variance of the following data: $6,8,10,12,14,16,18,20,22,24$

• A. $33$
• B. $30$
• C. $32$
• D. $35$

Answer 1

Answer: (A)

From the given data, we can form the following table. Let $A=14$

$x_i$	$y_i=\frac{x_i-14}{2}$	$\left(x_i-\bar{x}\right)$	${\left(x_i-\bar{x}\right)}^2$
6	-4	-9	81
8	-3	-7	49
10	-2	-5	25
12	-1	-3	9
14	0	-1	1
16	1	1	1
18	2	3	9
20	3	5	25
22	4	7	49
24	5	9	81
Total	5		330

Therefore, Mean $\bar{x}=$ assumed mean + $\frac{\sum _{i=1}^n{y}_i}{n}\times h$
$=14+\frac{5}{10}\times 2=15$
and varience $\left({\sigma }^2\right)=\frac{1}{n}\sum _{i=1}^{10}{\left(x_i\bar{x}\right)}^2$
$=\frac{1}{10}\times 330$
$=33$