Quandaries and Queries

Hi,

I have a question re: mean and median. I know what the difference is but just need some clarification on when you would use the mean and when you would use the median. Isn't it the case that with a skewed distribution the average (mean) would be higher or lower than the median, but with a normal distribution they would be very similar values?

If you have any examples to help explain this that would be greatly appreciated.

I am a teacher (of sorts!) and the person who is asking me the question is actually my boss!

Jan

Hi Jan,

Suppose that you are looking at the annual salary of professional hockey players and you calculate the mean X and the median Y. I would expect that X is considerably larger than Y since some hockey players make a great deal of money. If you were looking at the annual salary of teachers I would expect that the mean and median are quite close. The distribution of salaries of professional hockey players is skewed by the highly spayed players but the distribution of salaries of teachers is much more symmetric.

Here is an example with real data from Statistics Canada. The data is owned agricultural land by province in 2001.

 Province Hectares Newfoundland and Labrador 12,006 Prince Edward Island 193,248 Nova Scotia 353,739 New Brunswick 323,956 Quebec 2,852,943 Ontario 3,793,273 Manitoba 4,747,151 Saskatchewan 16,040,068 Alberta 12,424,756 British Columbia 1,525,437

Source: Statistics Canada, Census of Agriculture.

The mean is 4,226,657.7 hectares per province, but the median is 2,189,190 hectares per province. The large amount of agricultural land in Saskatchewan and Alberta skews the data. While the mean is more than 4 million hectares, half the provinces have less than 2 million hectares of owned agricultural land.

I hope this helps,
Penny

Go to Math Central