Mean from a frequency table

Here you will learn about the mean from a frequency table, including what it is and how to calculate it. You will also learn how to find an estimate for the mean from a grouped frequency table.

Students will first learn about mean from a frequency table as part of statistics and probability in $6$th grade.

What is mean from a frequency table?

Mean from a frequency table is when you find the mean average from a data set which has been organized into a frequency table. The frequency is the number of times a number or item is recorded in a data set.

To calculate the mean, find the total of the values and divide the total by the number of values. The number of values is the total frequency. This can be abbreviated to $n.$

You can use an extra column to help.

Mean is a measure of central tendency. It is a value that can be used to represent a set of data.

For example,

The frequency table shows the number of people living in $16$ apartments.

There are $5$ apartments with $1$ person living there, so calculate $1 \times 5=5$

There are $6$ apartments with $2$ people living there, so calculate $2 \times 6=12$

There are $3$ apartments with $3$ people living there, so calculate $3 \times 3=9$

There are $2$ apartments with $4$ people living there, so calculate $2 \times 4=8$

The number of values $(n)$ is the total frequency, here $n=16.$

$\text{Mean}=\cfrac{\text{total}}{n}=\cfrac{(1\times 5)+(2\times 6)+(3\times 3)+(4\times 2)}{16}=\cfrac{34}{16}=2.125$

The mean is $2.125$ people.

Estimated mean from a grouped frequency table

When the data has been grouped together and put into a grouped frequency table, you cannot find the actual mean because you only have a range of possible values.

Instead you can find an estimate for the mean using the midpoints of each group. You can add more columns to the grouped frequency table to help.

For example,

The frequency table shows the number of correct answers earned on a test by $20$ students.

There were $3$ people who answered between $0 \text{-}9$ questions correctly. As you don’t know the exact number of questions that each of these people got correct, you will use the midpoint of $4.5$ questions correct.

You can find the midpoint by adding the smallest value and the largest value together and dividing by $2.$

$\text{Estimated Mean}=\cfrac{\text{total}}{n}=\cfrac{420}{20}=21$

The estimated mean is $21$ questions correct.

What is mean from a frequency table?

Common Core State Standards

How does this relate to $6$th grade math?

• Grade 6: Statistics and Probability (6.SP.A.3)
  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

How to find the mean from a frequency table

In order to calculate the mean from a frequency table, you need to:

1. Multiply the number values by the frequencies.
2. Find the totals.
3. Divide the total by $\textbf{n}.$

Mean from a frequency table examples

Example 1: frequency table

The frequency table shows the number of goals scored in $10$ soccer games. Find the mean number of goals.

1. Multiply the number values by the frequencies.

You can add an extra column next to the frequency column to help find the subtotals.

2Find the totals.

Find the total of the frequency column, $n.$ Add up the subtotals to find the total.

3Divide the total by $\textbf{n}.$

The last step is to divide the total by $n.$

$\text{Mean}=\cfrac{\text{total}}{n}=\cfrac{11}{10}=1.1$

The mean is $1.1$ goals.

Example 2: frequency table

The frequency table shows the number of people on $20$ buses. Find the mean number of people.

Multiply the number values by the frequencies.

Show step

You can add an extra column next to the frequency column to help find the subtotals.

Find the totals.

Show step

Find the total of the frequency column, $n.$ Add up the subtotals to find the total.

Example 3: frequency table

The frequency table shows the ages, in years, of $25$ children in a math club. Find the mean age.

Multiply the number values by the frequencies.

Show step

You can add an extra column next to the frequency column to help find the subtotals.

Find the totals.

Show step

Find the total of the frequency column, $n.$ Add up the subtotals to find the total.

How to estimate the mean from a grouped frequency table

In order to estimate the mean from a grouped frequency table, you need to:

1. Find the midpoints of the groups.
2. Multiply midpoints by the frequencies.
3. Find the totals.
4. Divide the total by $\textbf{n}.$

Example 4: grouped frequency tables

The grouped frequency table shows the number of people in $10$ train carriages.

Estimate the mean number of people.

Find the midpoints of the groups.

Show step

You do not know the actual number of people in the groups, so use the midpoint.

Find the midpoint by adding the smallest value and the largest value together and dividing by $2.$ Add a column for the midpoints.

Multiply midpoints by the frequencies.

Show step

You can add an extra column next to the frequency column to help find the subtotals.

Find the totals.

Show step

Find the total of the frequency column, $n.$ Add up the subtotals to find the total.

Example 5: grouped frequency tables

The grouped frequency table shows the ages of $25$ people in a department store.

Estimate the mean age.

Find the midpoints of the groups.

Show step

You do not know the actual ages in the groups, so use the midpoint.

Find the midpoint by adding the smallest value and the largest value together and dividing by $2.$ Add a column for the midpoints.

Multiply midpoints by the frequencies.

Show step

You can add an extra column next to the frequency column to help find the subtotals.

Find the totals.

Show step

Find the total of the frequency column, $n.$ Add up the subtotals to find the total.

Example 6: grouped frequency tables

The grouped frequency table shows the weight in grams of $30$ potatoes.

Estimate the mean weight. Round your answer to the nearest tenths.

Find the midpoints of the groups.

Show step

You do not know the actual weights in the groups, so use the midpoint.

Find the midpoint by adding the smallest value and the largest value together and dividing by $2.$ Add a column for the midpoints.

Multiply midpoints by the frequencies.

Show step

You can add an extra column next to the frequency column to help find the subtotals.

Find the totals.

Show step

Find the total of the frequency column, $n.$ Add up the subtotals to find the total.

Teaching tips for mean from a frequency table

• Providing students with worksheets of practice problems is an easy way for them to practice finding the mean from a frequency table using given data values.

• Have students write step-by-step instructions in their math notebook while following example problems. You can also display the examples and instructions on an anchor chart that is displayed in the classroom for easy reference.

• Incorporate technology into the skill by allowing students to use Microsoft Excel or Google sheets to find formulas to find the mean.

Easy mistakes to make

• Finding median or mode instead of finding mean
  Check if you have been asked for the median, mode or mean average.

• Not dividing by the total frequency
  Remember to divide by the total frequency, not by the number of rows in the table. Always check to see if your final answer is sensible.

• Thinking the mean must be a whole number
  The mean does not have to be a whole number; it can also be a decimal or a fraction.

• Always estimating the mean from all frequency tables
  You only use the estimated mean when you have a grouped frequency table because you do not have the actual values for the data.

• Thinking a frequency table is different from a frequency distribution table
  A frequency distribution table is the same as a frequency table.

Related frequency table lessons

• Frequency table
• How to find the median from a frequency table
• Modal class

The next lessons are

• Frequency graph
• Types of sampling
• Probability
• Measurement and data
• Units of measurement

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