Question 1068455
there are two ways to get the variance.


the formulas they give you are:


s^2 = (x-m)^2/n


s^2 = sum(x^2)/n - m^2


s^2 = variance
x = data
m = mean
n = number of occurrences


here's a reference.


<a href = "http://www.sciencebuddies.org/science-fair-projects/project_data_analysis_variance_std_deviation.shtml" target = "_blank">http://www.sciencebuddies.org/science-fair-projects/project_data_analysis_variance_std_deviation.shtml</a>


the second formula is actually derived from the first and is a simpler way of calculating the variance.


the variance will be the same either way.


if you're dealing with just data (not frequency * data), it's fairly straight forward.


when you're dealing with frequency * data, it becomes a little bit more complicated and definitely more confusing.


when you're dealing with just data (not frequency * data), the formulas are:


m = sum(x)/n


s^2 = sum(x-m)^2/n


the alternate formula is:


s^2 = sum(x^2)/n - m^2


when you're dealing with frequency * data, as in your data set, the formulas become:


m = sum(f*x) / sum(f)


s^2 = sum (f*(x-m)^2)/sum(f)


the alternate formula becomes:


s^2 = sum (f*x^2)/sum(f) - m^2 ***** see note 1 immediately following.


***** note 1.
the subtraction of m^2 was missing in the formula presented earlier.
the formula is correct now.
the picture below has also been corrected.
the actual formula used was correct.
it was, unfortunately, not displayed correctly before.
it is now.


the following picture of the excel spreadsheet i used to do the calculations is shown below.


<img src = "http://theo.x10hosting.com/2017/021702.jpg" alt="$$$" </>


your variance, based on these calculations, should be 185.6394 rounded to the nearest decimal place.