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# Mode

## Number or numbers occurring the most often.

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Mode

Do you know what a mode is? When you have a set of data, you can figure out the mode. Let's think about Tania and her carrots.

Here is Tania’s data about the number of carrots picked each week over nine weeks of harvest.

2, 8, 8, 14, 9, 12, 14, 20, 19, 14

What number of carrots was picked most often?

This is what you will learn in this Concept. You will learn about the mode.

### Guidance

The mode of a set of data is simply the number that occurs most often. When we put our data in numerical order, it becomes easy to see how often each of them occurs.

Let’s look at the data set below.

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

First, we put the data in numerical order.

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

Now we look for any numbers that repeat.

Both 54 and 60 appear in the data set more than once. Which appears more often?

54 repeats the most times. That is our mode.

What if a data set doesn’t have a repeating number?

If no number occurs 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.

How can we use the mode to analyze data?

Because it is the number that occurs most often in a data set, we know that it is the most frequent answer to our question or result of our experiment.

Now let's practice. Find the mode of each data set.

#### Example A

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

Solution: 4

#### Example B

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

Solution: 9

#### Example C

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

Solution: 23

Now back to the original problem. Here is Tania’s data about the number of carrots picked each week over nine weeks of harvest.

2, 8, 8, 14, 9, 12, 14, 20, 19, 14

Which number of carrots was harvested the most often?

To answer this question, we need to reorder the data to find the mode or the number that occurs the most often.

2, 8, 8, 9, 12, 14, 14, 14, 19, 20

The number 14 occurs the most often, that is the mode of this data set.

### 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

### Guided Practice

Here is one for you to try on your own.

Suppose the data below shows how many people visit the zoo each afternoon.

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

We can see that 91 occurs most often in the set, so we know 91 is the mode.

This number helps us approximate how many people visit the zoo each afternoon because it was the most frequent number.

### Practice

Directions: 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

### 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.
Frequency

Frequency

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

Maximum

The largest number in a data set.
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.
Median

Median

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

Minimum

The minimum is the smallest value in a 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.