A sample size is denoted n, and the population size is denoted N.  We then have

 

 

The Median

 

The median is the middle number when a set of data is written in order when there are an odd number of data.

 

For example for 2, 5, 7, 11, 23, 31, 40, 40, 42 the median is 23

 

When there are an even number of data the median is the average of the middle two values

 

For example for 2, 5, 7, 11, 23, 31,  the median is (7 + 11)/2 = 9

 

The Mode

 

For our purposes the mode is fairly useless.  It is the most frequently appearing data value.

 

For example for 2, 5, 7, 11, 23, 31, 40, 40, 42 the mode is 40.  More on the mode

 

The Midrange

 

The midrange is the value half way between the highest and lowest values, or it is the average of those two values.

 

 

Weighted Means (or weighted averages)

 Suppose you are judging a science project, the project is to be judged on originality, how well it is put together and how well it works.  However the three items judged do not carry the same weight.  Suppose originality is weighted 5, how well it is put together is weighted 2 and how well it works is weighted 4.

To evaluate this you multiply each score by its weight and then divide by the sum of the weights.  Suppose scores were 9 for originality, 7 for how well it is put together and 3 for how well it works.  Then

                   Your grade as a weighted mean.

 

The Mean for a Frequency Distribution and the Modal Class

 

Suppose you wish to calculate a mean from a frequency distribution.  Since you do not know the exact values an exactly correct answer is not possible, so you do the best you can do.

 

Consider the following:

 

Class       Frequency

9.5 - 17.5        4

17.5 - 25.5      1

25.5 - 33.5      3

33.5 - 41.5      5

41.5 - 49.5      1