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# 2.20: Mode

Difficulty Level: At Grade Created by: CK-12
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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.

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 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 mode for this set.

### 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.

Find the mode of each data set.

#### Example 3

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.

#### Example 4

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 mode for a number that occurs most often.

The answer is there is no mode.

#### Example 5

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.

### Review

Identify the mode for the following sets of data.

1. 2, 3, 3, 3, 2, 2, 2, 5, 6, 7

2. 4, 5, 6, 6, 6, 7, 3, 2

3. 23, 22, 22, 24, 25, 25, 25

4. 123, 120, 121, 120, 121, 125, 121

5. 678, 600, 655, 655, 600, 678, 600, 600

6. 4, 5, 4, 5, 3, 3

7. 6, 7, 8, 3, 2, 4, 4, 7, 7, 7

8. 11, 10, 9, 13, 14, 16, 11, 10, 11

9. 21, 23, 25, 22, 22, 27

10. 27, 29, 29, 32, 30, 32, 31

11. 34, 35, 34, 37, 38, 39, 39, 34, 34

12. 43, 44, 43, 46, 39, 50, 43, 43

13. 122, 100, 134, 156, 144, 110, 110

14. 224, 222, 220, 222, 224, 224

15. 540, 542, 544, 550, 548, 547, 547, 550, 550, 548

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

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

bimodal

If there are two numbers that occur equally frequently in a set of data, then the data is said to be bimodal.

Frequency

In statistics, the frequency of an event is the number of times that event occurred.

Maximum

The largest number in a data set.

Mean

The mean of a data set is the average of the data set. The mean is found by calculating the sum of the values in the data set and then dividing by the number of values in the data set.

Median

The median of a data set is the middle value of an organized data set.

Minimum

The minimum is the smallest value in a data set.

Mode

The mode of a data set is the value or values with greatest frequency in the data set.

multimodal

When a set of data has more than 2 values that occur with the same greatest frequency, the set is called multimodal    .

normal distribution curve

A normal distribution curve is a symmetrical curve that shows the highest frequency in the center with an identical curve on either side of the center.

trimodal

A trimodal set has three modes and may be also referred to as multimodal.

unimodal

If a data set has only 1 value that occurs most often, the set is called  unimodal.

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