Question

The number of books read by 8 student sharing a month are 2,5,8,11,14,6,12,10, calculate the standard deviation​

Answer 1

Answer:

The standard deviation of the data is 3.741.

Step-by-step explanation:

Given : The no. of books read by 8 students during a month are 2,5,8,11,14,6,12,10.

To find : Calculate standard deviation of the data ?

Solution :  

The standard deviation we have to follow the steps :

Step 1 - Calculate the average mean of the data

i.e. $\bar{x}=\frac{\sum x_n}{n}$    

$\bar{x}=\frac{2+5+8+11+14+6+12+10}{8}$

$\bar{x}=\frac{68}{8}$

$\bar{x}=8.5$

Step 2 -  Subtracting each number from the mean and squaring the difference,

$(2-8.5)^{2} = (-6.5)^{2} = 42.25$

$(5-8.5)^{2} = (-3.5)^{2} = 12.25$

$(8-8.5)^{2} = (-0.5)^{2} = 0.25$

$(11-8.5)^{2} = (2.5)^{2} = 6.25$

$(14-8.5)^{2} = (5.5)^{2} = 30.25$

$(6-8.5)^{2} = (-2.5)^{2} = 6.25$

$(12-8.5)^{2} = (3.5)^{2} = 12.25$

$(10-8.5)^{2} = (1.5)^{2} = 2.2$

Step 3 - Mean of the squared differences

$\sum (x-\bar{x})^2=\frac{42.25+12.25+0.25+6.25+30.25+6.25+12.25+2.25}{8}$

$\sum (x-\bar{x})^2=\frac{112}{8}$

$\sum (x-\bar{x})^2=14$

Step 4 - The standard deviation of the data is

$s=\sqrt{14}$

$s=3.741$

Therefore, The standard deviation of the data is 3.741.