Topics
8. Statistics
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United States of America
Grade 6

8.02 Frequency and mode

Lesson
Practice

Introduction

We have looked at what questions we should ask when gathering different types of data. Now we are going to look at how tables can be used to help us organize and interpret data.

Tables, frequencies, and modes

When conducting a survey, the three main steps are:

  1. Gathering the data

  2. Organizing the data

  3. Interpreting the data

When representing the frequency of different results in our data, we often choose to use a frequency table.

A frequency table communicates the frequency of each result from a set of data. Typically the far left column describes the result or data value and any columns to the right represent frequencies or how many times a result occurred.

The frequency of a result is the number of times that it appears in the list of data.

The mode of a data set is the result with the greatest frequency. If there are multiple results that share the greatest frequency then there will be more than one mode.

Examples

Example 1

Yvonne asks 15 of her friends what their favorite color is. She writes down their answer. Here is what she wrote down: \text{Blue, Pink, Blue, Yellow, Green, Pink, Pink, Yellow,}\\ \text{ Green, Blue, Yellow, Pink, Yellow, Pink, Pink}

a

Count the number of each color and complete the table.

\text{Color}\text{Number of} \\\ \text{Friends}
\text{Pink}
\text{Green}
\text{Blue}
\text{Yellow}
Worked Solution
Create a strategy

Count the number of times Yvonne wrote each color.

Apply the idea
\text{Color}\text{Number of} \\\ \text{Friends}
\text{Pink}6
\text{Green}2
\text{Blue}3
\text{Yellow}4
b

Which color is the mode?

Worked Solution
Create a strategy

Choose the color that has the largest number.

Apply the idea

The mode of the data is pink.

Example 2

Thomas conducted a survey on the average number of hours his classmates exercised per day and displayed his data in the table below.

\text{No. exercise} \\ \text{hours}\text{ Frequency}
02
112
27
35
40
53
a

How many classmates did Thomas survey?

Worked Solution
Create a strategy

To find the number of classmates surveyed, add all the frequencies of the results.

Apply the idea
\displaystyle \text{Classmates surveyed}\displaystyle =\displaystyle 2+12+7+5+0+3Add all the frequencies
\displaystyle =\displaystyle 29Evaluate
b

What is the mode of the data?

Worked Solution
Create a strategy

Choose the result with the greatest frequency in the data.

Apply the idea

1 hour of exercise is the mode because it has the greatest frequency.

c

How many classmates exercised for less than three hours?

Worked Solution
Create a strategy

Add the frequencies of the results that represent less than three hours of exercise.

Apply the idea
\displaystyle \text{No. classmates}\displaystyle =\displaystyle 2+12+7Add the frequencies
\displaystyle =\displaystyle 21Evaluate
d

How many classmates exercised for at least three hours?

Worked Solution
Create a strategy

Add the frequencies of the results representing three or more hours of exercise.

Apply the idea
\displaystyle \text{No. classmates}\displaystyle =\displaystyle 5+0+3Add the frequencies
\displaystyle =\displaystyle 8Evaluate
Idea summary

The frequency of a result is the number of times that it appears in the list of data.

The mode of a data set is the result with the greatest frequency. If there are multiple results that share the greatest frequency then there will be more than one mode.

Outcomes

6.SP.B.5

Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5.A

Reporting the number of observations

6.SP.B.5.B

Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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