# Statistics: sample variance help!?

find the range, mean, variance and standard deviation of the sample data set.

18 12 6 11 16 9 7 13 8

18 , 12 , 6 , 11 , 16 , 9 , 7 , 13 and 8

Range :

[ Range : The largest value - the smallest value ]

The largest value in the list is 18

Aand the smallest value is 6

So the range is 18 - 6 = 12

Mean :

The mean is the usual average

So (18+12+6+11+16+9+7+13+8) / 9

Simplify

= 100 / 9

= 11.1111

Variance :

To calculate the variance follow these steps:

• Work out the mean (the simple average of the numbers)
• Then for each number: subtract the Mean and square the result (the squared difference).
• Then work out the average of those squared differences.

Mean = 11.111

Variance σ^2 = [(18-11.111)²+(12-11.111)²+(6-11.111)²+(11-11.111)²+(16-11.111)²+(9-11.111)²+(7-11.111)²+(13-11.111)²+(8-11.111)²] / 9

Simplify

σ^2 = [ (6.889)²+(0.889)²+(-5.111)²+(-0.111)²+(4.889)²+(-2.111)²+(-4.111)²+(1.889)²+(-3.111)² ] / 9

Simplify

σ^2 = [ (47.458321)+(0.790321)+(26.122321)+(0.012321)+(23.902321)+(4.456321)+(16.900321)+(3.568321)+(9.678321)] / 9

Simplify

σ^2 = 132.888889 / 9

σ^2 = 14.7654321111

There fore Variance σ^2 = 14.7654321111

Standard deviation :

The Standard Deviation is just the square root of Variance,

So  σ = √(14.7654321111)

Simplify

σ = 3.84258144

σ = 4 (to the nearest)