Question

the no of books read by 8 students during a month are 2,5,8,11,14,6,12,10. calculate standard deviation of the data .


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Answer 1

Answer:

0

Step-by-step explanation:

Mean = 68/8 = 8.5

Standard deviation = (2-8.5) + (5-8.5) + (8-8.5) + (11-8.5) + (14-8.5) + (6-8.5) + (12-8.5) + (10-8.5)

= -6.5 + -3.5 + -0.5 + 2.5 + 5.5 + -2.5 + 3.5 + 1.5

= 0

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Answer 2

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 :

To get the standard deviation we have to follow the steps :

Calculate the average mean of the data

i.e. $\bar{x}=\frac{\sum x_n}{n}$

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

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

$\bar{x}=8.5$

Subtracting each number from the mean and squaring the difference,

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

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

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

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

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

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

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

$(10-8.5)^{2} = (1.5)^{2} = 2.25$

Mean of the squared differences

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

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

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

The standard deviation of the data is

$s=\sqrt{14}$

$s=3.741$

Therefore, The standard deviation of the data is 3.741.