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# Mode

## Number or numbers occurring the most often.

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Mode

Remember the sled dogs from the Median Concept? Well, let's look at the speeds once again.

Alaskan sled dogs travel varying speeds during the Iditarod. These strong, wonderful animals can travel at an average speed of anywhere from 5 to 15 miles per hours.

Here are some speeds from the last Iditarod.

10 mph

12 mph

8 mph

15 mph

9 mph

8 mph

7 mph

12 mph

Which speed is the mode of this data set?

This Concept is about figuring out the mode of a data set. You will be able to answer this question by the end of the Concept.

### Guidance

Previously we worked on finding the mean and the median, now we can find the mode of a set of data too.

The mode is the value that occurs the most times in a set of data.

Mode sounds like most and that can be an easy way to remember it.

Let’s look at how to find the mode.

The chart below depicts the daily temperature in San Diego for the first seven days in August. Determine the mode for this set of data.

Date: Temperature:
Sunday 8/1 $88^\circ F$
Monday 8/2 $83^\circ F$
Tuesday 8/3 $87^\circ F$
Wednesday 8/4 $89^\circ F$
Thursday 8/5 $82^\circ F$
Friday 8/6 $79^\circ F$
Saturday 8/7 $87^\circ F$

To find the mode, look for the number that occurs most often. In this case, 87 is the mode because it appears twice in the set of data.

The mode is $87^\circ F$ .

Now we can find the mode of a set of test scores.

Katie’s first four test scores are 75%, 81%, 80%, and 84%. Determine the mode of Katie’s test scores.

In this case, there is not one number that occurs more than another. Therefore, there is no mode.

Mode = none

Here is another situation where the mode is a useful tool in analyzing data.

Miguel measured the height of eight students in his class in inches. Determine the mode of his classmate’s heights.

$51 \quad 45 \quad 47 \quad 51 \quad 50 \quad 56 \quad 52 \quad 50$

In this case, there are two data values that appear most often, 51 and 50.

The modes of Miguel’s data are 51 and 50.

Name the mode of each data set.

#### Example A

$2, 3, 3, 5, 6, 7, 8, 9, 3$

Solution: $3$

#### Example B

$12, 15, 67, 45, 44, 88, 90$

Solution: No Mode

#### Example C

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

Solution: $67$

Here is the original problem once again.

Alaskan sled dogs travel varying speeds during the Iditarod. These strong, wonderful animals can travel at an average speed of anywhere from 5 to 15 miles per hours.

Here are some speeds from the last Iditarod.

10 mph

12 mph

8 mph

15 mph

9 mph

8 mph

7 mph

12 mph

Which speed is the mode of this data set?

There are two speeds that occurred the most in this data set.

The first one is 8 mph - a rather slow speed.

The second one is 12 mph - a rather fast speed.

### Guided Practice

Here is one for you to try on your own.

Name the mode in this data set.

2, 4, 5, 6, 2, 3, 4, 2, 2, 2, 7, 8, 9

Remember, when looking for the mode, we are looking for the value that occurs the most times.

The mode of this set of values is 2.

### Explore More

Directions: 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

### Vocabulary Language: English

bimodal

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

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

Frequency

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

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

Mode

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

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

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

trimodal

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

unimodal

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