# Solving Average Standard Deviation

Introduction :

Standard deviation measures about the average of statistical population, a data set, or a probability distribution from the square root of its variance. Standard deviation is a distributedly helps us to calculate the deviation or dispersion, being algebraically more tractable though practically less robust than average absolute deviation. In standard deviation solving average is helps us to measure, about the average of low standard deviation which indicates that the data points tend to be very close to the mean, and also measure the average of high standard deviation which indicates that the data spread over a large range of values.
Solving Average Standard Deviation:

Standard deviation average solving is the process which is similar to finding the mean of the standard deviation.Formula for solving the mean of the standard deviation is given below,

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

variance =   `((sum(x - barx)^2)) / (n-1)`

Standard deviation: S =  `sqrt(((sum(x - barx)^2)) / (n-1))`
Example for Solving Average Standard Deviation:

Example for solving average standard deviation 1:

Here are 5 percentage 95, 93, 97, 99, 91. Solving the given percentages find the standard deviation.

Solution:

Average,

` barx`  =  ` ( sum(x) ) / n`

= `(95 + 93 + 97 + 99 + 91) / 5`

= `475 / 5`

= 95

Standard Deviation,

S  = `sqrt(((sum(x - barx)^2)) / (n-1))`

= ` sqrt(( ( 95 - 95 )^2 + ( 93 - 95 )^2 + ( 97 - 95 )^2 + ( 99 - 95 )^2 + (91 - 95)^2) / (5 - 1))`

=`sqrt((( 0 )^2 + ( -2 )^2 +( 2 )^2 + ( 4 )^2 + (-4)^2 )/ 4) `

=  `sqrt(40 / 4) `

S   = `sqrt(10)`

Answer: Standard Deviation ` S = 3.1622`

Thus, solving average standard deviation method is explained.

Example for solving average standard deviation 2:   Calculate the mean and standard deviation for the given dataset.
`i`    `x`
1    93
2    97
3    99

Solution:

`barx` = `( 91 + 95 + 99) / 3`

= `285/3 `

= 95
`x`       `x - barx`     ` ( x - barx)^2`
91    91 - 95 = -4
16
95    95 - 95 = 0
0
99    99 - 95 = 4
16

` (x - barx)^2` = 32

S =  `sqrt( 32 / 2 )`

S =  `sqrt(16)`

` S = 4 `