Question

14. Runs scored by batsman in 5 one day matches are 50, 70, 82, 93, and 20. The standard deviation is
A. 25.79
B. 25.49
C. 25.29
D. 25.69​

Answer 1

Answer:

25.79 IS THE ANSWER

Step-by-step explanation:

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Answer 2

Given :

• Number of matches (n) = 5
• Scores = 50,70,82,93 and 20

To find : The standard deviation.

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

First of all we have to calculate the mean of the scores.

Mean = (Sum of all scores) ÷ (n)

Or,

Mean = (50+70+82+93+20)÷5

Mean = 315 ÷ 5

Mean = 63

Now, the standard deviation can be calculated by the following formula :

$Standard \: \: \: deviation = \sqrt{ \frac{Σ \: (x - mean)^2}{(n)} }$

Here, x = each value of score

n = number of matches

mean = mean of all scores

So,

The standard deviation will be :

$= \sqrt{ \frac{(50 - 63)^2 + (70 - 63)^2 + (82 - 63)^2 + (93 - 63)^2 + (20 - 63)^2}{5} }$

$= \sqrt{ \frac{ ( - 13)^2 + (7)^2 + (19)^2 + (30)^2 + ( - 43)^2}{5} }$

$= \sqrt{ \frac{169+49+361+900+1849}{5} }$

$= \sqrt{ \frac{3328}{5} }$

$= \sqrt{665.6}$

$= 25.79$

(This will be considered as the final result.)

Hence, the standard deviation will be 25.79 (option A)