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subject: Standard Deviation Shows [print this page]

Introduction to standard deviation shows:

In statistics, the standard deviation shows about the statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though practically less robust than average absolute deviation. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data spread over a large range of values.

Standard Deviation Shows:

Standard deviation shows that the variation for the given set of datas. This Standard deviation shows the variation from population, a data set, and probability distribution etc

Formulas to which shows the standard deviation are,

Mean: 'barx' = '( sum(x) ) / n'

Standard deviation: S =' sqrt(((sum(x - barx)^2)) / (n-1))'

By using these formulas we can able to shows the variations for the set of data's.

Example for the Standard Deviation Shows:

Example for standard deviation shows 1: Here are 4 measurements 56, 57.,51 and 55. Calculate standard deviation for the given measurements

Solution:

Average, Mean

' barx' = '(56 + 57 + 52 + 55) / 4'

= '220 / 4'

= 55

Standard Deviation,

S = ' sqrt(( ( 56 - 55 )^2 + ( 57 - 55 )^2 + ( 51 - 55 )^2 + ( 55 - 55 )^2) / (4 - 1))'

= 'sqrt((( 1 )^2 + ( 2 )^2 +( -3 )^2 + ( -0 )^2 )/ 3) '

= 'sqrt(14 / 3) '

S = 'sqrt(4.66667)'

Standard Deviation 'S = 2.1602'

Answer: Thus the Standard Deviation ' S = 2.1602' is shows the deviation from the given data's.

Example for standard deviation shows 2: there were a data set with 4 values as 76, 70, 71 and 75. Calculate shows the standard deviation

Solution:

Average, Mean

' barx' = '(77 + 71 + 73 + 75) / 4'

= '296 / 4'

= 74

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Standard Deviation,

S = ' sqrt(( ( 77 - 74)^2 + (71 - 74 )^2 + ( 73 - 74 )^2 + ( 75 - 74 )^2) / (4 - 1))'

= 'sqrt((( 3 )^2 + ( -3 )^2 +( -1 )^2 + ( 1 )^2 )/ 3) '

= 'sqrt(20 / 3) '

S = 'sqrt(6.66667)'

Standard Deviation 'S = 2.581'

Answer: Thus the Standard Deviation ' S = 2.581''is shows the deviation from the given data's.'

Example for standard deviation shows 3: Calculate the mean and standard deviation for the given dataset.

i X

1 2400

2 3800

3 4900

4 5700

5 6500

6 7400

Solution:

'barx' = '( 2400 + 3800 + 4900 + 5700 + 6500 + 7400) / 6' = 5116

'x' 'x - barx' ' ( x - barx)^2'

2400 2400 - 5116 = -2716 7376656

3800 3800 - 5116 = -1316 1731856

4900 4900 - 5116 = -216 46656

3700 5700 - 5116 = -584 341056

6500 6500 - 5116 = 1384 1915456

7400 7400 - 5116 = 2284 5216656

' (x - barx)^2' =16628336

S = 'sqrt( 16628336 / 5 )'

S = 'sqrt( 3325667.2 )'

' S = 1823.64119'

Answer:

'barx' ' = 4116'

'S = 1823.64119'

Thus, the Standard Deviation shows that the data set has found.

by: Omkar Nayak

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