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# Mode

## Number or numbers occurring the most often.

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### License: CC BY-NC 3.0 [Figure1]

Mrs. Jones has ten children in her class, ranging from age 5 to 7. She wants to find the most common age of the students in her class, so she has asked them all their exact age and made a list:

5, 7, 5, 5, 6, 7, 7, 6, 5, 6

How can Mrs. Jones find the most common age among her students?

In this concept, you will learn how to calculate mode.

### Calculating Mode

Data is a set of numerical or non-numerical information. Data can be analyzed in many different ways. In this concept you will analyze numerical data using the mode.

Mode is the numerical value that occurs most frequently in a data set.

To calculate the mode, look for the value that occurs most often.

Let's look at an example.

Find the mode of the data set:  47, 56, 51, 45, 56, and 41.

First, sort the data from least to greatest.

41, 45, 47, 51, 56, 56

Next, look at the data set and find the value that occurs most often. In this data set the number 56 occurs twice. This is the mode.

The answer is the mode is 56.

### Examples

#### Example 1

Earlier, you were given a problem about Mrs. Jones and her class.

Mrs. Jones asked her students their ages and has made a list so that she can calculate the mode age.

5, 7, 5, 5, 6, 7, 7, 6, 5, 6

First, list the data from smallest to largest.

5, 5, 5, 5, 6, 6, 6, 7, 7, 7

Next, determine which age occurs the most frequently.

In this case, 5 occurs four times.

The answer is the mode age of Mrs. Jones class is 5 years old.

#### Example 2

The chart below shows the daily temperature in San Diego for the first seven days in August. Calculate the mode temperature.

San Diego Temperatures in August
Date: Temperature:
Sunday 8/1 88F\begin{align*}88^\circ F\end{align*}
Monday 8/2 83F\begin{align*}83^\circ F\end{align*}
Tuesday 8/3 87F\begin{align*}87^\circ F\end{align*}
Wednesday 8/4 89F\begin{align*}89^\circ F\end{align*}
Thursday 8/5 82F\begin{align*}82^\circ F\end{align*}
Friday 8/6 79F\begin{align*}79^\circ F\end{align*}
Saturday 8/7 87F\begin{align*}87^\circ F\end{align*}

First, arrange the data from smallest to largest.

79, 82, 83, 87, 87, 88, 89

Next, look at the data to find which values occur most often. In this case, 87F\begin{align*}87^\circ F\end{align*} occurs twice, which means it is the mode.

The answer is the mode is 87F\begin{align*}87^\circ F\end{align*}

#### Example 3

Find the mode of the following data set.

13,13,45,45,67,89,13,67,67,67,13\begin{align*}13, 13, 45, 45, 67, 89, 13, 67, 67, 67, 13\end{align*}

First, order the data from least to greatest.

13, 13, 13, 13, 45, 45, 67, 67, 67, 67, 89

Next, look at the data set to determine which values occur most often. In this case 13 and 67 each occur four times.

The answer is the mode is 13 and 67.

#### Example 4

John wants to know his mode quiz grade based on the following scores.

78, 90, 83, 88, 67, 91, 84, 69, 56

First, order the data from smallest to largest.

56, 67, 69, 78, 83, 84, 88, 90, 91

Next, look at the data set to determine which values occur most often. In this case, no value is repeated.

The answer is there is no mode.

#### Example 5

Miguel measured the height of eight students in his class in inches. Find the mode of the heights below.

5145475150565250\begin{align*}51 \quad 45 \quad 47 \quad 51 \quad 50 \quad 56 \quad 52 \quad 50\end{align*}

First, sort the data from smallest to largest.

45, 47, 50, 50, 51, 51, 52, 56

Next, look at the data set to determine which values occur most often. In this set, 50 and 51 each occur twice.

The answer is the mode of Miguel's classmate heights are 50" and 51".

### Review

Identify the mode for the following sets of data.

1. 2, 3, 3, 3, 2, 2, 2, 5, 6, 7, 7, 7, 7
2. 4, 5, 6, 6, 6, 7, 3, 2, 6, 5, 5
3. 23, 22, 22, 24, 25, 25, 25, 21, 20, 22, 27
4. 123, 120, 121, 120, 121, 125, 121, 121
5. 678, 600, 655, 655, 600, 678, 600, 600
6. 4, 5, 4, 5, 3, 3, 4, 4, 4, 4, 6
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, 21, 22, 21, 21
10. 27, 29, 29, 32, 30, 32, 31, 33, 33, 33, 33
11. 34, 35, 34, 37, 38, 39, 39, 34, 34
12. 43, 44, 43, 46, 39, 50, 43, 43, 51, 51
13. 122, 100, 134, 156, 144, 110, 110
14. 224, 222, 220, 222, 224, 224, 221, 222, 223, 225
15. 540, 542, 544, 550, 548, 547, 547, 550, 550, 548

To see the Review answers, open this PDF file and look for section 11.3.

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### 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.

Data

Data is information that has been collected to represent real life situations, usually in number form.

Frequency

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

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.

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.