Describing Data with Averages

Describing Data with Averages

These describe the center or typical value in a dataset. This is also called as measures of central tendency.

There are three commonly used measures for central tendency

1) Mean

2) Median and

3) Mode

Let us discuss them one by one with the help of examples

1) Mean : The mean can be defined as sum of all the values divided by total number of values. The formula for mean is

 Mean = ∑X / N

For example ‒

Consider the data as 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Mean = (10+20 + 30+ 40+ 50+ 60+ 70+80+ 90 + 100)/10 = 55

2) Median : It is basically the middle value when the data is arranged.

For example ‒

Consider odd number of elements 5, 10, 15, 20, 25, 30, 35 the median is 20

Consider even number of elements 5, 10, 15, 20 the median is (10+ 15) / 2 = 12.5

3) Mode: The mode is the value that occurs frequently in the dataset. If each element appears only once in the dataset then there is no mode. plow vis

For example ‒ 1, 2, 3, 5, 5, 5, 6 here the mode is 5.

Review Questions

1. Which measure of central tendency is most affected by extreme values?

2. In what situations would you prefer using the median instead of the mean?