How to do a Variance Table Problem
33
36
38
33
42
You're given a set of either n = 5 or n = 7 delicious pieces of data, like this:
First, you're asked to compute measures of centrality: the mean, median, and mode of these data.

To get the mean, you add up the data and divide by n.
 \(\mu\) = (33+36+38+33+42)/5 = 36.4

The get the median, sort the data in order and find the middle value.
 33 33 36 38 42
 36 is the median.

The mode is the most popular value. There can be none at all or more than one, but I make sure there is one, and only one.
 In this data set, 33 is the most commonly occurring value. It be the mode.
 33 33 36 38 42
Then you have to calculate measures of dispersion. These are range, variance, and standard deviation.

Range is calculated by subtracting the smallest value from the largest value.
 42  33 = 9.
 The range is 9.
 Variance and standard deviation are calculated using a variance table. The variance table breaks down the following formula for variance into steps:
33  
36  
38  
33  
42 
The data are listed in the first column. The mean of the data, as we've already calculated, is \(\mu\) = 36.4.
Now fill out the second column by subtracting \(\mu\) from each value.
\(X\)
\(X  \mu\)
\(\Sigma (X  \mu)^2\)
33  33  36.4 = 3.4  
36  36  36.4 = 0.4  
38  38  36.4 = 1.6  
33  33  36.4 = 3.4  
42  42  36.4 = 5.6 
\(\mu\) = 36.4
Now square the values in this second column and put the results in the third column. These are your squares.
\(X\)
\(X  \mu\)
\( (X  \mu)^2 \)
33  3.4  (3.4)² = 11.56 
36  0.4  (0.4)² = 0.16 
38  1.6  (1.6)² = 2.56 
33  3.4  (3.4)² = 11.56 
42  5.6  (5.6)² = 31.36 
\(\mu\) = 36.4
Now add up those squared values to get the sum of squares, \(\Sigma (X  \mu)^2\).
\(X\)
\(X  \mu\)
\( (X  \mu)^2 \)
33  3.4  11.56 
36  0.4  0.16 
38  1.6  2.56 
33  3.4  11.56 
42  5.6  31.36 
\(\mu\) = 36.4
\(X\)
\(X  \mu\)
\( (X  \mu)^2 \)
Sum of squares = \(\Sigma (X  \mu)^2\) = 57.2
The \(\Sigma\) symbol means summation, i.e., add up all the squares.
33  3.4  11.56 
36  0.4  0.16 
38  1.6  2.56 
33  3.4  11.56 
42  5.6  31.36 
\(\mu\) = 36.4
\(X\)
\(X  \mu\)
\( (X  \mu)^2 \)
Sum of squares = \(\Sigma (X  \mu)^2\) = 57.2
Divide the sum of squares by n to get the variance.
 Variance = \(\sigma^2 = \frac{57.2}{5} \) = 11.44
33  3.4  11.56 
36  0.4  0.16 
38  1.6  2.56 
33  3.4  11.56 
42  5.6  31.36 
\(\mu\) = 36.4
\(X\)
\(X  \mu\)
\( (X  \mu)^2 \)
Sum of squares = \(\Sigma (X  \mu)^2\) = 57.2
Variance = \(\sigma^2 = \frac{57.2}{5} \) = 11.44
Finally, take the square root of the variance to get the standard deviation.
 Standard deviation = \(\sigma\) = 3.38231
Mean =  36.4 
Median =  36 
Mode =  33 
Range =  9 
Variance =  11.44 
Standard Deviation =  3.38231 
So now we have all the answers to the variance table problem:
Plus, you have to have a filledout table.
Have Fun.
Doing a Variance Table Problem
By smilinjoe
Doing a Variance Table Problem
 211