Question

v) The variance of two observations 10 and 17 is
(A) 12.25
(B) 12
(C) 1.225
(D) 13​

Answer 1

Answer:

the answer is option a 12.25

hope it helps you

Answer 2

The variance of two observations 10 and 17 is 12.25

Given :

Two observations 10 and 17

To find :

The variance of two observations 10 and 17 is

(A) 12.25

(B) 12

(C) 1.225

(D) 13

Solution :

Step 1 of 2 :

Write down given observations

Here the given two observations are 10 and 17

Step 2 of 2 :

Find the variance

The required variance

$\displaystyle \sf{ = \frac{ { \sum x_i}^{2} }{n} - { \bigg( \frac{ \sum x_i}{n} \bigg)}^{2} }$

Since there are two observations

So n = 2

Hence the required variance

$\displaystyle \sf{ = \frac{ { \sum x_i}^{2} }{2} - { \bigg( \frac{ \sum x_i}{2} \bigg)}^{2} }$

$\displaystyle \sf{ = \frac{ {10}^{2} + {17}^{2} }{2} - { \bigg( \frac{ 10 + 17}{2} \bigg)}^{2} }$

$\displaystyle \sf{ = \frac{ 100 + 289 }{2} - { \bigg( \frac{ 27}{2} \bigg)}^{2} }$

$\displaystyle \sf{ = \frac{ 389 }{2} - { (13.5 )}^{2} }$

$\displaystyle \sf{ = 194.5 - 182.25 }$

$\displaystyle \sf{ = 12.25}$

Hence the correct option is (A) 12.25

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