Clark plays on his high school basketball team. Every game, their player statistics are kept track of and Clark reviews the amount of points he scores each game. Here are Clark's points scored for each game this season:

12, 17, 11, 13, 14, 22, 11, 13, 17, 13, 14, 13, 19, 12

Clark wants to know which amount of points he scored most often this season. To do this, Clark needs to see which number of points shows up most often in his data set.

In this concept, you will learn how to find the mode of a set of data.

### Mode

The **mode** of a set of data is simply the number that occurs most often. Putting the data in numerical order makes it easy to see how often each value in the data set occurs.

Here is an example:

61, 54, 60, 59, 54, 51, 60, 53, 54

First, put the data in numerical order.

51, 53, 54, 54, 54, 59, 60, 60, 61

Next, look for any numbers that repeat. Both 54 and 60 appear in the data set more than once. The mode is only which value appears the most.

Then, choose the value that appears most in the data set.

The answer is 54.

If there aren't any numbers that occur more than once, or if numbers appear in the set the same number of times, the set has no single mode.

22, 19, 19, 16, 18, 21, 30, 16, 27

In the set above, both 16 and 19 occur twice. No number in the set happens the *most* often, so there is no single mode for this set (since there are exactly two modes, this set may be called *bimodal*).

### Examples

#### Example 1

Earlier, you were given a problem about Clark and his basketball points.

He wants to figure out which number of points in a game he has scored most often. Here are Clark's statistics:

12, 17, 11, 13, 14, 22, 11, 13, 17, 13, 14, 13, 19, 12

What is the mode of Clark's data?

First, Clark puts his points in numerical order from least to greatest.

11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 17, 17, 19, 22

Next, Clark looks for repeating scores in his data set. Clark has multiple points that he scored in more than one game: 11, 12, 13, 14, and 17.

Then, Clark looks for the scored points that occurs most often in his data set. Clark scored 13 points in 4 different games.

The answer is 13. This is the point value Clark scored in games most often.

#### Example 2

Suppose the data below shows how many people visit the zoo each afternoon. What amount of people is the most frequent number of visitors. In other words, what is the mode of the data set?

68, 104, 91, 80, 91, 65, 90, 91, 70, 80

First, put the numbers in numerical order.

65, 68, 70, 80, 80, 90, 91, 91, 91, 104

Next, look for numbers in the data set that repeat. Both 80 and 91 repeat in the data set.

Then, choose the number in the data set that occurs the most. 91 occurs 3 times whereas 80 occurs 2 times.

The answer is 91.

#### Example 3

Find the mode of the following data set.

2, 4, 4, 4, 6, 7, 8, 8, 10, 10, 11, 12

First, put the data in numerical order. This data set is already in numerical order.

Next, look for repeating numbers in the data set. Multiple numbers repeat in this data set: 4, 8, 10.

Then, choose the number that occurs most in the data set. Four occurs more than 8 and 10 does.

The answer is 4.

#### Example 4

Find the mode of the following data set.

5, 8, 9, 1, 2, 9, 8, 10, 11, 18, 19, 20

First, put the data in numerical order.

1, 2, 5, 8, 8, 9, 9, 10, 11, 18, 19, 20

Next, look for repeating numbers in the data set. The numbers 8 and 9 both repeat in the set.

Then, choose the number that occurs most in the data set. In this case, 8 and 9 occur the same number of times; therefore, there is no single mode for a number that occurs most often.

The answer is there is no single mode.

#### Example 5

Find the mode of the following data set.

12, 12, 5, 6, 7, 11, 23, 23, 67, 23, 89, 23

First, put the data in numerical order.

5, 6, 7, 11, 12, 12, 23, 23, 23, 23, 67, 89

Next, look for repeating numbers in the data set. The numbers 12 and 23 both repeat in this data set.

Then, choose the number that occurs most in the data set. The number 12 occurs twice while 23 repeats four times.

The answer is 23.

### Review

Identify the mode for the following sets of data.

- 2, 3, 3, 3, 2, 2, 2, 5, 6, 7
- 4, 5, 6, 6, 6, 7, 3, 2
- 23, 22, 22, 24, 25, 25, 25
- 123, 120, 121, 120, 121, 125, 121
- 678, 600, 655, 655, 600, 678, 600, 600
- 4, 5, 4, 5, 3, 3
- 6, 7, 8, 3, 2, 4, 4, 7, 7, 7
- 11, 10, 9, 13, 14, 16, 11, 10, 11
- 21, 23, 25, 22, 22, 27
- 27, 29, 29, 32, 30, 32, 31
- 34, 35, 34, 37, 38, 39, 39, 34, 34
- 43, 44, 43, 46, 39, 50, 43, 43
- 122, 100, 134, 156, 144, 110, 110
- 224, 222, 220, 222, 224, 224
- 540, 542, 544, 550, 548, 547, 547, 550, 550, 548

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.20.