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## Key Concepts

- Make a frequency table and a histogram.
- Use a frequency table to solve problems.
- Use a histogram to solve problems.

## Display data in frequency tables and histograms

### Introduction

In this chapter, we will learn to make a frequency table and a histogram, using a frequency table to solve problems and using a histogram to solve problems.

### Frequency table

Frequency refers to the number of times an event or a value occurs. For example, if four students have a score of 85 in science, then the score of 85 is said to have a frequency of 4.

A frequency table shows the number of times a value occurs in each category or interval.

We use tally marks to count the frequency of occurrence of something:

### Histogram

A histogram is the most commonly used graph to show frequency distributions. It is a graph that uses bars to show the number of values in each category or interval. The bars of a histogram always touch.

Example of a histogram:

### Make a frequency table and a histogram

**Example 1:**

Ms. Annette surveyed a group of students who entered a school science fair and recorded the number of hours spent on their projects in the table shown. She wants to analyze the hours spent. What is one way that Ms. Annette can organize the data?

**Solution:**

**Step 1**

Ms. Annette can set up time intervals for the data.

**Step 2**

Count the number, or frequency, of times for each interval.

**Step 3**

Make a frequency table with the data.

**Step 4**:

She can use the frequency table to make a histogram.

Display the data by drawing a bar for each interval.

### Use a frequency table to solve problems

**Example 2:**

The following frequency table shows the number of popcorn bags sold each day at a movie theatre.

- Is the greatest number of bags sold being between 50 and 59?
- Is the lowest number of bags being sold between 40 and 49?
- How many bags are sold between 40 and 59?

**Solution:**

- Is the greatest number of bags being sold between 50 and 59?

The greatest frequency is 7, which corresponds to bags sold between 50 – 59. However, the greatest number of bags being sold is between 60 and 69. - Is the lowest number of bags being sold between 40 and 49?

The lowest frequency is 0, which corresponds to bags sold between 40 – 49. However, the lowest number of bags sold is between 30 and 39. - How many bags are sold between 40 and 59?

The number of bags sold between 40 and 49 is 0.

The number of bags sold between 50 and 59 is 7.

Hence, the number of bags sold between 40 and 59 is 0 + 7 = 7.

**Example 3:**

The following frequency table shows the length of selected movies shown in a popular theater over the past 6 months.

- How many movies being shown are between 130 and 139 minutes?
- How many movies being shown are between 90 and 109 minutes?
- Is the greatest number of movies being shown are between 100 and 109 minutes?
- Are there more movies with a length between 80 and 99 minutes than between 130 and 149 minutes?

**Solution:**

- How many movies being shown are between 130 and 139 minutes?

3 movies are shown with a length between 130 and 139 minutes. - How many movies being shown are between 90 and 109 minutes?

4 movies are shown with a length between 90 and 99 minutes.

7 movies are shown with a length between 100 and 109 minutes.

Hence, the number of movies shown between 90 and 109 minutes is 4 + 7 =11. - Is the greatest number of movies being shown are between the range of 100 and 109 minutes?

7 movies are shown between the range of 100 and 109 minutes. Also, 7 movies are shown

between 120 and 129 minutes. - Are there more movies with a length between 80 and 99 minutes than between 130 and 149 minutes?

1 movie is shown between the range of 80 and 89 minutes.

4 movies are shown between the range of 90 and 99 minutes.

Hence, the total number of movies shown between 80 and 99 minutes is 1 + 4 =5.

3 movies are shown between the range of 130 and 139 minutes.

1 movie is shown between the range of 140 and 149 minutes.

Hence, the total number of movies shown between 130 and 149 minutes is 3 + 1 = 4.

Yes, there are more movies with a length between 80 and 99 minutes than between 130 and

149 minutes.

### Use a histogram to solve problems

**Example 4:**

The histogram shows the number of marks scored by students in a math class test.

- How many students took the math test?
- How many more students had scores that were 80 or lower than students who had scores that were higher than 90?
- How many more students had scores that were 80 or lower than students who had scores that were higher than 90?

**Solution:**

- How many students took the math test?

The total number of students can be found by adding the number of students shown by each bar.

4 + 6 + 0 + 8 + 7 + 2 = 27

- How many more students had scores that were 80 or lower than students who had scores that were higher than 90?

The number of students with scores 80 or lower is

4 + 6 = 10

The number of students with scores above 90 is

7 + 2 = 9

- Can you tell from the histogram how many students scored 83 on the test?

There is no bar on the histogram for 81 – 85 scores.

## Exercise

**Fill in the blanks**:

A _________________ shows the number of times a value occurs in each category or interval.

A ___________________ is a graph that uses bars to show the number of values in each category or interval.

- A data set contains ages of people in a colony ranging from 7 to 28. 7, 12, 10, 14, 19, 16, 22, 16, 18, 25, 28, 13 Complete the frequency table.

- Make a frequency table of the data in intervals.

- Make a histogram of the data.

- Display the following data in a histogram.

- Sandra recorded the time in minutes that she took to complete her homework each morning for one month.

5, 7, 9, 10, 10, 11, 13, 14, 15, 15, 18, 19, 20, 20, 22, 26, 29, 31, 33, 35, 38, 40, 40, 42, 49, 50, 51, 55, 58, 72

Use the data given to complete the histogram.

- Ms. Carolyn, a P.E. teacher in a school, recorded the number of sit-ups the students in her class did in one minute.

- How many students did sit-ups between 30 and 39?
- How many students did sit-ups between 40 and 59?
- What is the total number of students in Ms. Carolyn’s class?

- The following frequency table shows the number of marks obtained by a class.

- Is the greatest number of marks obtained between the range of 10 and 15?
- Is the lowest number of marks obtained between the range of 0 and 5?

- Gary measured the heights of 20 boys in a class and created the following frequency table.

- Is the greatest height measured between the range of 145 and 150?
- Is the lowest height measured between the range of 155 and 160?

- The following histogram represents the weights, rounded to the nearest pound, of several orders of dog food.

- What is the total number of dog food ordered?
- How many orders are placed in the weight ranging between 11 and 15?

### Concept Map

### What have we learned

- Make a frequency table to organize the data
- Make a histogram using the frequency table
- Solve problems using frequency table on histogram

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