Subject: What is the difference between Mean and Average?

Hi my name is Julie,

What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower)

Thank you very much!

The term "average" usually encompasses several ways to measure what value best represents a sample. There are various measurements that are used and at times the term and measurement used depends on the situation.

A statistician or mathematician would use the terms mean and average to refer to the sum of all values divided by the total number of values, what you have called the average. This especially true if you have a list of numbers. In fact even in mathematics there are different "averages" or "means" and this one is more properly called the arithmetic mean.

The quantity obtained by adding the largest and smallest values and dividing by 2, statisticians call the midrange. There are times however that this is called the mean. For example the weather office records the "mean daily temperature", which is the sum of the high temperature and the low temperature divided by 2.

The median is the central point of a data set. To find the median, you would list all data points in ascending order and simply pick the entry in the middle of that list.

If this is not enough there is another measure. The mode is the value that occurs most often.

For example, consider the following data points: 1,1,2,3,4

The mean or average is (1+1+2+3+4)/5 = 2.2
The median is "2" (the central value).
The mode is "1" (it occurs most often).
The midrange is (4+1)/2 = 2.5

Hope this helps,
Patrick and Penny