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How to find the population mean,standard deviation and the variance for...

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jora7 | Student, Undergraduate | Honors

Posted February 14, 2012 at 3:30 AM via web

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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

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tahasiddiqui8 | Student, Undergraduate | eNotes Newbie

Posted February 14, 2012 at 4:51 AM (Answer #1)

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mean(x bar)=(summation of x)/n(total no of terms(data))

mean=12+8+10+11+7+10+15+13+14+9/10

mean=109/10

mean=10.9

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 :

Regards:

TAHA SIDDIQUI

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted February 14, 2012 at 9:09 PM (Answer #2)

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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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