Essay on Introduction for Solving Standard Deviation Formula

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Introduction for solving standard deviation formula:

In Statistics, the standard deviation is named as the determination of indecision of a chance variable, expressed as the average deviation of a group of data from its arithmetic mean and planned as the positive square root of the inconsistency. In this article we are discuss about solving standard deviation formula problems. The following formula for solving standard deviation.

[S = sqrt ((sum(X -M)^2)/(N-1))]

M – Mean of given values.

N – Total number of values.

X – Specified value.
Example problems for solving standard deviation formula:

Solving standard
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Solution:

(i) Calculate the mean and standard deviation for the specified values.

X = 26, 34, 33, 31.

Mean (M) = [(26+ 34 + 33 + 31) / 4]

= [124/4]

= 31

(ii) Then we can calculate the sum of (X - M) 2

X

X-M

(X-M)2

26

26-31 = -5

25

34

34-31 = 3

9

33

33-31 = 2

4

31

31-31 = 0

0

Total

38

N = 4 is the sum number of specified values.

Then N -1 = 4 - 1

= 3

(iii) Apply values in standard deviation formula:

[S = sqrt((sum(X - M)^2) /(N-1))]

= [sqrt(38)/sqrt (3)]

= [ 6.1644/1.73]

= 3.56

The answer is: 3.56

Solving standard deviation formula- Example 3

Find the standard deviation for following values 26, 34, 19, 24, 20 and 33.

Solution:

(i) Find the mean and deviation for the given values.

X = 26, 34, 19, 24, 20 and 33.

M = [ (26 + 34 + 19 + 24 + 20 + 33)/ 6]

= [156/6]

= 26

(ii) Then we can find the sum of (X - M) 2

X

X-M

(X-M)2

26

24-26 = 0

0

34

34-26 = 8

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