LESSON: Mean, Median, and Mode

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Introduction

Mean, Median and Mode 

In this lesson, you will learn how to use the following skills.

  • Find the mean of a set of data.
  • Find the median of a set of data.
  • Find the mode of a set of data.
  • Identify the range of a set of data.
  • Select the best average to represent given sets of data.

Vocabulary 

Mean
the average of a set of numbers. The mean gives us a good overall assessment of a set of data.
Maximum
the greatest score in a data set
Minimum
the smallest score in a data set
Median
the middle score in a data set
Mode
the number or value that occurs most often in a data set
Range
the difference between the smallest value in a data set and the greatest number in a data set
Measures of Central Tendency
a way of selecting which value in a data set best expresses the set of data.

READ: Find the Mean of a Set of Data

Find the Mean of a Set of Data

The first way of analyzing data that we are going to learn about is called the mean. A more common name for the mean of a set of data is to call it the average. In other words, the mean is the average of the set of data. An average lets us combine the numbers in the data set into one number that best represents the whole set. 

There are two steps to finding the mean.

  1. We add up all of the numbers in the data set.
  2. We divide the total by the number of numbers in the set.


Example

10, 7, 3, 8, 2

First, we need to add all the numbers together.

10 + 7 + 3 + 8 + 2 = 30

Now we divide the total, 30, by the number of items in the set. There are 5 numbers in the set, so we divide 30 by 5.

30 \div 5 = 6

The mean, or average, of the set is 6.


Let's see how finding the mean helps us interpret data. Suppose we want to know how tall plants grow when we add a certain nutrient to the water.

Example:

The data below shows the height in inches of 10 plants grown with the nutrient-rich water.

9, 10, 7, 3, 11, 9, 8, 11, 7, 10

Let’s find the mean. Add up all of the numbers first.

9 + 10 + 7 + 3 + 11 + 9 + 8 + 11 + 7 + 10 = 85

Now we divide by the number of items in the data set. There are 10 plants, so we get the following answer.

85 / 10 = 8.5

The mean height of the plants is 8.5 inches. This gives us a nice estimate of how tall a plant might grow with the nutrient-rich water.


Let’s see where the mean falls in relation to the other numbers in the set.

If we reorder the numbers, we get

3, 7, 7, 8, 9, 9, 10, 10, 11, 11

The minimum of the set is 3 and the maximum is 11. Take a good look at all of the numbers in the set.


Here are some conclusions that we can draw from this data.

  • Only 3 stands out by itself at one end of the data set. Since it is much smaller than the other numbers, we might assume that this plant didn’t grow very well for some reason.

We can make a prediction based on this.

  • Perhaps of the 10 plants it got the least light, or maybe its roots were damaged.

The mean helps even out any unusual results such as the height of this one plant.