How To Find Population Mean
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` .
Here is how to solve for the standard deviation.
mean(x bar)=(summation of x)/n(total no of terms(data))
standard deviation(s) formula listed below with all explained variables so by putting the values you will get the solution.
x is data values as you mentioned above.
x bar is called mean I have find above.
so subtract mean from each data value and taking their square and finally add all results bz we have summation in formula.
and then divide the whole result after summation by n, where n in your data is 10 and finally take their root so you will get standard deviation.
variance(s^2) formula given below.
I hope you will now easily calculate variance by using the above formula, in above formula all right side variables are known you have to put their values and get a result.
best of luck :