Mean Median Mode and Range

The mean median mode and range all are values that help characterize a data set. Mean is technically called the arithmetic mean. The mean median mode and range each represent different types of averages of the data set.

Mean :

Consider an example. Jim went bowling and each of his scores for 5 games is shown in the table below. Thus, these 5 scores represent the data set of observations.

To determine the mean, we have to add the data values (or scores) and then divide by the total number of values (games). Thus,

Mean = (20+24+33+55+28) / 5 = 160 / 5 = 32

Since the mean is 32, this indicates that you expect that if Jim bowled the 6th game, his score would be 32.

Median :

Another type of average is called the median but the median is not the exact average. It separates the lower and upper half of observations.

To find the median in the above example,

1. arrange the scores in ascending order, 20, 24,28,33,55
2. Select the middle number which is 28.

So the median here is 28

If the total numbers are even, say the above game has 6th row and the score is 34 then,

1. Arrange the scores in ascending order, 20,24,28, 33, 34, 55. The middle numbers are 33 and 34
2. Find the average of these two numbers. (33 + 34) / 2 = 67/2 = 33.5

So the median is 33.5

Mode :

The mode is the number that occurs the most frequently among the observations. As there is no number in the above data set that occurs maximum times there is no mode in the above data set.

Say Jim had 6th bowling game with a score of 24 then the data set would look like 20, 24, 33, 55, 28, 24 ( 20, 24, 24, 28, 33, 55 after rearranging). As the score 24 has occurred twice while other scores have just occurred once, the mode is 24.

Say if Jim had played 7th bowling game with a score of 33, the scores of seven games after rearranging would look like 20, 24, 24, 28, 33, 33, 55

Here the numbers 24 and 33 have occurred twice which is the maximum in this case. So there are two modes 24 and 33 and hence called bimodal.

Range:

Range is the difference between lowest and highest observation.

In the above example, the lowest observation is 20 and the highest is 55. So the range is 55 – 20 = 35