Question 1190485: -5
3
-5
-5
-3
-3
-3
Calculate the value of the sample variance.
Answer by math_tutor2020(3835)   (Show Source):
You can put this solution on YOUR website!
First we add up all the values
(-5)+(3)+(-5)+(-5)+(-3)+(-3)+(-3) = -21
Then divide by n = 7 because there are 7 items in this list
-21/n = -21/7 = -3
The sample mean is xbar = -3
Next, we subtract xbar from each item
-5 - xbar = -5 - (-3) = -2
3 - xbar = 3 - (-3) = 6
-5 - xbar = -5 - (-3) = -2
-5 - xbar = -5 - (-3) = -2
-3 - xbar = -3 - (-3) = 0
-3 - xbar = -3 - (-3) = 0
-3 - xbar = -3 - (-3) = 0
Perhaps it's better to use a table to organize the data values
| x | x-xbar | | -5 | -2 | | 3 | 6 | | -5 | -2 | | -5 | -2 | | -3 | 0 | | -3 | 0 | | -3 | 0 |
The next step is to square each item in the second column to form the column (x-xbar)^2
| x | x-xbar | (x-xbar)^2 | | -5 | -2 | 4 | | 3 | 6 | 36 | | -5 | -2 | 4 | | -5 | -2 | 4 | | -3 | 0 | 0 | | -3 | 0 | 0 | | -3 | 0 | 0 |
Add up everything in the third column:
4+36+4+4+0+0+0 = 48
Then divide by n-1 = 7-1 = 6 to compute the sample variance
48/(n-1) = 48/6 = 8
Such a process is fairly tedious busywork if you are dealing with large data sets.
I recommend using a calculator such as this one
https://www.calculatorsoup.com/calculators/statistics/variance-calculator.php
and this is a handy tool to check your work.
To compute the standard deviation, you apply the square root to the variance
Standard Deviation = sqrt(variance)
Answer: 8
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