Answer: 2.12
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Work Shown
Add up the values
sum = 10+10+9+8+10+5+6+4+8+4
sum = 74
Divide that sum by the sample size n = 10 to get the mean
mean = sum/n
mean = 74/10
mean = 7.4
From here we subtract the mean from each data value. Use absolute value bars to ensure the result is not negative.
|x1 - mean| = |10 - 7.4| = 2.6
|x2 - mean| = |10 - 7.4| = 2.6
|x3 - mean| = |9 - 7.4| = 1.6
|x4 - mean| = |8 - 7.4| = 0.6
|x5 - mean| = |10 - 7.4| = 2.6
|x6 - mean| = |5 - 7.4| = 2.4
|x7 - mean| = |6 - 7.4| = 1.4
|x8 - mean| = |4 - 7.4| = 3.4
|x9 - mean| = |8 - 7.4| = 0.6
|x10 - mean| = |4 - 7.4| = 3.4
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The list of deviations are: {2.6, 2.6, 1.6, 0.6, 2.6, 2.4, 1.4, 3.4, 0.6, 3.4}
This is a list of distances each data value is from the mean.
Example: The data value 10 is 2.6 units from the mean 7.4
The idea from here is to find the mean of these deviations.
So we'll add them up and divide by 10
(2.6+2.6+1.6+0.6+2.6+2.4+1.4+3.4+0.6+3.4)/10 = 21.2/10 = 2.12
Final Answer: 2.12