# How To Find Population Mean

How to find the population mean,standard deviation and the variance for 12,8,11,10,7,10,15,13,14 and 9.Find mean, standard deviation and variance

You need to work on simple average of the numbers to evaluate the mean such that:

Mean = `(12+8+11+10+7+10+15+13+14+9)/10`

Mean = `109/10` => Mean = 10.9

You need to evaluate the variance first and then you may evaluate the standard deviation since the standard deviation is the square root of...

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You need to work on simple average of the numbers to evaluate the mean such that:

Mean = `(12+8+11+10+7+10+15+13+14+9)/10`

Mean = `109/10` => Mean = 10.9

You need to evaluate the variance first and then you may evaluate the standard deviation since the standard deviation is the square root of variance.

You need to remember that variance, `sigma^2` , expresses the mean of squared differences from mean such that:

`sigma^2 = ((12-10.9)^2 + (8-10.9)^2 + (11-10.9)^2 + (10-10.9)^2 + (7-10.9)^2 + (10-10.9)^2 + (15-10.9)^2 + (13-10.9)^2 + (14-10.9)^2 + (9-10.9)^2)/10`

`sigma^2 = (1.21 + 8.41 + 0.01 + 0.81 + 15.21 + 0.81 + 16.81 + 4.41 + 9.61 + 3.61)/10` `sigma^2 = (60.9)/10 = 6.09`

You may find the stadard deviation, hence:

`sigma = sqrt(6.09) =gt sigma = 2.467`

Hence, evaluating the mean, variance and standard deviation for the numbers 12,8,11,10,7,10,15,13,14,9 yields: Mean = 10.9, Variance=`sigma^2 = 6.09` , standard deviation=`sigma=2.467` .

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