Question

For a set of 50 observations, the sum of their
squares is 3050, the standard deviation of
these observation
is 5. What is their arithmetic
mean?

9
8
7
6​

Answer 1

Step-by-step explanation:

999999999999999999999

Answer 2

The arithmetic mean = 6

Given :

For a set of 50 observations, the sum of their squares is 3050, the standard deviation of these observation is 5.

To find :

The arithmetic mean

9

8

7

6

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that for a set of 50 observations, the sum of their squares is 3050, the standard deviation of these observation is 5.

By the given

n = 50

$\sf \sum \: {x}^{2} = 3050$

$\sf \sigma = 5$

Step 2 of 2 :

Find the arithmetic mean

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

$\displaystyle \sf{ \implies 5 = \sqrt{ \frac{ 3050 }{50} - { \bigg( \frac{ \sum x}{n} \bigg)}^{2} } }$

$\displaystyle \sf{ \implies \sqrt{ 61 - { \bigg( \frac{ \sum x}{n} \bigg)}^{2} } = 5}$

$\displaystyle \sf{ \implies 61 - { \bigg( \frac{ \sum x}{n} \bigg)}^{2} = {5}^{2} }$

$\displaystyle \sf{ \implies 61 - { \bigg( \frac{ \sum x}{n} \bigg)}^{2} = 25 }$

$\displaystyle \sf{ \implies { \bigg( \frac{ \sum x}{n} \bigg)}^{2} = 61 - 25 }$

$\displaystyle \sf{ \implies { \bigg( \frac{ \sum x}{n} \bigg)}^{2} = 36 }$

$\displaystyle \sf{ \implies { \bigg( \frac{ \sum x}{n} \bigg)}^{} = 6}$

The arithmetic mean = 6

Hence the correct option is 6