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subject: Standard Deviation Rule [print this page]

Introduction to Standard deviation rule:
Introduction to Standard deviation rule:

In standard deviation, generally standard deviation is used to find out the variation of the given set of data's or the stastical report of population etc... Standard deviation rule involves that the deviation of the given number is find out by having a rul or procedure to follow. Standard deviation rule is used to find the deviation step by step. First we have to find the mean of the given data, after that varience using varience formula when squaring the varience then standard deviation is obtained.

Example for Standard Deviation Rule:

Example for standard deviation rule: Find the standard deviation for the given set of numbers { 54.5, 55.3, 56.7, 49, 53.5 } using the rule.

Solution:

Step 1: Mean

Mean = ' ( 54.5+ 55.3 + 56.7 + 49 + 53.5 ) / 5 '

= '269 / 5'

= 53.8

Step 2: Variance

Variance = '( (54.5 - 53.8)^2 + (55.3 - 53.8)^2 + (56.7 - 53.8)^2 + (49 - 53.8)^2 + (53.5 - 53.8 )^2 )/(5-1)'

= '( (0.7)^2 + (1.5)^2 + (2.9)^2 + (-4.8)^2 + (-0.3)^2 )/4'

= '(0.83+1.22+1.702+2.190+0.54)/4'

= '6.482/4'

= 1.62

Step 3:Standard deviation

Standard deviation = 'sqrt (1.62)'

= 1.27

More Problem for Standard Deviation Rule:

Example for standard deviation rule 1:

Calculate the standard deviation using standard deviation rule for the given values 8, 5, 3 and 16.

Solution:

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

X = 10, 5, 4, 17

M = '(10 + 5 + 4 + 17)/4'

= '36/4'

= 9

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

X

X-M

(X-M)2

10

5

4

17

10-8 = 2

5-8 = -3

4-8 = -4

17-8 = 9

4

9

16

81

Total

110

N = 4 is the total number of given values.

Then N-1 = 4-1

= 3

(iii) To locate the standard deviation by the method.

S = 'sqrt((X-M)^2/(N-1))'

= '(sqrt110)/(sqrt3)'

= '10.488/1.73'

= 6.062

Example for standard deviation rule 2:

Calculate the standard deviation using standard deviation rule for the given values 5, 1, 11, 17 and 8.

Solution:

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

X = 5, 1, 11, 17, 8

M = '(5 + 1 + 11 + 17 + 8)/5'

= '40/5'

= 8

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

X

X-M

(X-M)2

5

1

11

17

8

5 - 8 = -3

1 - 8 = -7

11 - 8 = 3

17 - 8 = 9

8 - 8 = 0

9

49

9

81

0

Total

148

N = 5 is the total number of given values.

Then N-1 = 5-1

= 4

(iii) For calculate standard deviation the method is shown.

S = 'sqrt((X-M)^2/(N-1))'

= '(sqrt148)/(sqrt4)'

= '12.165/2'

= 6.08

by: johnharmer

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