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# Frequency Tables to Organize and Display Data

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How long is the Iditarod? Do you know? Take a look at this dilemma.

Jasper is curious about how many days it takes a musher to finish the Iditarod. Looking online, he has discovered that the average is from 10 – 15 days, but that isn’t specific enough for him.

“I want to know more details about it,” he tells Mr. Hawkins first thing on Monday morning.

“Well, you have to narrow down your findings. I would suggest you look at the final standings from 2010. Then you can create a frequency table and a histogram.”

“Alright, that’s a good idea,” Jasper says.

Jasper begins his research on the Iditarod website. He makes notes on the number of days that it took the mushers in the 2010 Iditarod to finish.

1 musher took 8 days 18 mushers took 9 days 16 mushers took 10 days 6 mushers took 11 days 9 mushers took 12 days 4 mushers took 13 days

Jasper wants to organize this data in a frequency table. However, he is stuck on how to do it. Do you know? This Concept will teach you all about creating frequency tables using given data. By the end of the Concept, you will understand how to help Jasper.

### Guidance

Previously we worked on different ways to display data. In this Concept, you will learn about frequency tables and histograms. Let’s start by looking at frequency tables.

What is a frequency table?

A frequency table is another way of summarizing data. A frequency table depicts the number of times a data value occurs.

A frequency table is created by making a table with three separate columns. One column is designated for intervals. The amount of intervals is determined by the range in data values. If the range in data values is not that great, the intervals will be small. If the range in data values is great, the intervals will be larger. It is important that the intervals are of equal size and do not overlap.

Another column is created for tallied results. This is where you tally the number of times you see a data value from each interval.

In the last column, add the tally marks to determine the frequency results.

Let’s look at how we can apply this information.

Twenty people were asked to state the number of hours they sleep each night. The results of the survey are listed below. Create a frequency table to display the data.

7, 8, 6, 9, 10, 12, 5, 7, 8, 9, 10, 11, 12, 7, 6, 7, 8, 10, 11, 9

Step 1: Make a table with three separate columns.

• Intervals
• Tallied results
• Frequency results

In this case, there is not a wide range in data values, therefore the intervals will be displayed by ones.

Step 2: Looking at the data, tally the number of times a data value occurs.

Step 3: Add the tally marks to record the frequency.

Number of Hours Slept Tally Frequency
5 I 1
6 I I 2
7 I I I I 4
8 I I I 3
9 I I I 3
10 I I I 3
11 I I 2
12 I I 2

Now you can see how arranging the data in this way makes it much easier to follow.

The data below depicts the amount of time (in minutes) 20 middle school students spent on the computer each day. Arrange the data on a frequency table.

10, 32, 8, 55, 5, 0, 30, 20, 25, 45, 40, 60, 45, 15, 5, 56, 47, 12, 15, 20

Step 1: Make a table with three separate columns.

• Intervals
• Tallied results
• Frequency results

In this case, there is not a wide range in data values, therefore the intervals will be displayed by ones.

Step 2: Looking at the data, tally the number of times a data value occurs.

Step 3: Add the tally marks to record the frequency.

Number of Minutes on the Computer Tally Frequency
0 – 5 I I I 3
6 – 10 I I 2
11 – 15 I I I 3
16 – 20 I I 2
21 – 25 I 1
26 – 30 I 1
31 – 35 I 1
36 – 40 I 1
41 – 45 I I 2
46 – 50 I 1
51 – 55 I 1
56 – 60 I I 2

Once again, the tally marks in the frequency table can give you a clear picture of the data.

Look at the frequency table above and answer the following questions.

#### Example A

How many students spent 51 – 55 minutes on the computer?

Solution: 1

#### Example B

How many students spent 0 – 5 minutes on the computer?

Solution: 3

#### Example C

How many students spent 41 – 45 minutes on the computer?

Solution: 2

Now let's go back to Jasper and the frequency table. Here is the original problem once again.

Jasper is curious about how many days it takes a musher to finish the Iditarod. Looking online, he has discovered that the average is from 10 – 15 days, but that isn’t specific enough for him.

“I want to know more details about it,” he tells Mr. Hawkins first thing on Monday morning.

“Well, you have to narrow down your findings. I would suggest you look at the final standings from 2010. Then you can create a frequency table and a histogram.”

“Alright, that’s a good idea,” Jasper says.

Jasper begins his research on the Iditarod website. He makes notes on the number of days that it took the mushers in the 2010 Iditarod to finish.

1 musher took 8 days 18 mushers took 9 days 16 mushers took 10 days 6 mushers took 11 days 9 mushers took 12 days 4 mushers took 13 days

Using this data, Jasper can create a frequency table with three different columns. One that says "Days", one that says "Frequency" and one that says "Total". Here is the table he can use.

Days Tally Frequency
8 1 1
9 11111 18
11111
11111
111
10 11111 16
11111
11111
1
11 11111 6
1
12 11111 9
1111
13 1111 4

### Vocabulary

Frequency Table
a table that keeps track of the number of times a data value occurs.

### Guided Practice

Here is one for you to try on your own.

The data on the table below depicts the height (in meters) a ball bounces after being dropped from different heights. Create a frequency table to display the data.

$6 \quad 9 \quad 4 \quad 12 \quad 11 \quad 5 \quad 7 \quad 9 \quad 13 \quad 5 \quad 6 \quad 10 \quad 14 \quad 7 \quad 8$

First arrange the data on a frequency table.

Recall that a table with three columns needs to be drawn: one for intervals, one for tallied results, and another for frequency results. The range in values for this set of data is nine. Therefore, data will be tallied in intervals of two.

Bounce Height Tally Frequency
3 – 4 I 1
5 – 6 I I I I 4
7 – 8 I I I 3
9 – 10 I I I 3
11 – 12 I I 2
13 – 14 I I 2

### Practice

Directions: Use each set of data to answer the following questions.

Here is a list of the number of days that 7th students at Marrimack Middle School bought lunch.

0 Days = 15 students

1 Day = 13 students

2 Days = 30 students

3 Days = 21 students

4 Days = 35 students

5 Days = 60 students

1. How many students are in the $7^{th}$ grade?

2. What is the most popular number of days?

3. What is the least popular number of days?

4. Create a frequency table to show the data.

5. Were any students left out of the count?

6. How do you know?

7. Create a frequency table to display the data below.

2, 5, 3, 1, 6, 5, 7, 8, 3, 1

8. Were there any numbers not represented?

9. What is the most popular number or numbers?

Directions : The following frequency table shows data regarding the number of people who attended different movies in one week. Use the following frequency table to answer each question.

# of People at the movies per week Frequency
20 4
50 3
85 3
90 5
120 2

10. If we were to create a list of this data, is the following list correct or incorrect?

20, 20, 20, 20, 50, 50, 50, 90, 90, 90, 85, 85, 85, 120, 120

11. Would you consider the list in number 1 to be organized or unorganized data?

12. How many showings had 90 people or more in attendance?

13. How many showings had less than 50 people in attendance?

14. How many showings had less than 70 people in attendance?

15. True or false. This data also tells you which showings had the most people in attendance.

16. True or false. There were two showings that had 78 people in attendance.