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 katex is not definedth 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 katex is not defined

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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 katex is not defined apartments.

There are katex is not defined apartments with katex is not defined person living there, so calculate katex is not defined

There are katex is not defined apartments with katex is not defined people living there, so calculate katex is not defined

There are katex is not defined apartments with katex is not defined people living there, so calculate katex is not defined

There are katex is not defined apartments with katex is not defined people living there, so calculate katex is not defined

The number of values katex is not defined is the total frequency, here katex is not defined

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katex is not defined

The mean is katex is not defined people.

[FREE] Mean from a Frequency Table Worksheet (Grade 6 to 8)

[FREE] Mean from a Frequency Table Worksheet (Grade 6 to 8)

[FREE] Mean from a Frequency Table Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 to 8 students’ understanding of mean from a frequency table. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE
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[FREE] Mean from a Frequency Table Worksheet (Grade 6 to 8)

[FREE] Mean from a Frequency Table Worksheet (Grade 6 to 8)

[FREE] Mean from a Frequency Table Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 to 8 students’ understanding of mean from a frequency table. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

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 katex is not defined students.

There were katex is not defined people who answered between katex is not defined 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 katex is not defined questions correct.

You can find the midpoint by adding the smallest value and the largest value together and dividing by katex is not defined

Mean from frequency table Image 3 US

katex is not defined

The estimated mean is katex is not defined questions correct.

What is mean from a frequency table?

What is mean from a frequency table?

Common Core State Standards

How does this relate to katex is not definedth 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 katex is not defined

Mean from a frequency table examples

Example 1: frequency table

The frequency table shows the number of goals scored in katex is not defined soccer games. Find the mean number of goals.

Mean from frequency table Image 4 US

  1. Multiply the number values by the frequencies.

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

Mean from frequency table Image 5 US

2Find the totals.

Find the total of the frequency column, katex is not defined Add up the subtotals to find the total.

Mean from frequency table Image 6 US

3Divide the total by katex is not defined

The last step is to divide the total by katex is not defined

katex is not defined

The mean is katex is not defined goals.

Example 2: frequency table

The frequency table shows the number of people on katex is not defined buses. Find the mean number of people.

Mean from frequency table Image 7 US

Multiply the number values by the frequencies.

Find the totals.

Divide the total by katex is not defined

Example 3: frequency table

The frequency table shows the ages, in years, of katex is not defined children in a math club. Find the mean age.

Mean from frequency table Image 10 US

Multiply the number values by the frequencies.

Find the totals.

Divide the total by katex is not defined

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 katex is not defined

Example 4: grouped frequency tables

The grouped frequency table shows the number of people in katex is not defined train carriages.

Estimate the mean number of people.

Mean from frequency table Image 13 US

Find the midpoints of the groups.

Multiply midpoints by the frequencies.

Find the totals.

Divide the total by katex is not defined

Example 5: grouped frequency tables

The grouped frequency table shows the ages of katex is not defined people in a department store.

Estimate the mean age.

Mean from frequency table Image 17 US

Find the midpoints of the groups.

Multiply midpoints by the frequencies.

Find the totals.

Divide the total by katex is not defined

Example 6: grouped frequency tables

The grouped frequency table shows the weight in grams of katex is not defined potatoes.

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

Mean from frequency table Image 21 US

Find the midpoints of the groups.

Multiply midpoints by the frequencies.

Find the totals.

Divide the total by katex is not defined

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.

Practice mean from a frequency table questions

1. The frequency table shows the number of pets of katex is not defined students. Find the mean number of pets. Give your answer to the nearest hundredth.

 

Mean from frequency table Image 25.1 US

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

You need to multiply the numbers by the frequencies and find the total. Then divide the total by katex is not defined the frequency total,

 

Mean from frequency table Image 26 US

 

katex is not defined

2. The frequency table shows the number of puppies in katex is not defined litters. Find the mean number of puppies. Give your answer to the nearest hundredth.

 

Mean from frequency table Image 27.1 US

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

You need to multiply the numbers by the frequencies and find the total. Then divide the total by katex is not defined the frequency total.

 

Mean from frequency table Image 28 US

 

katex is not defined

3. The frequency table shows the price of a can of biscuits in katex is not defined different grocery stores. Find the mean price. Give your answer to the nearest tenth.

 

Mean from frequency table Image 29 US

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

You need to multiply the numbers by the frequencies and find the total. Then divide the total by katex is not defined the frequency total.

 

Mean from frequency table Image 30 US

 

katex is not defined

4. The grouped frequency table shows the number of children in katex is not defined families. Estimate the mean number of children. Give your answer to the nearest hundredth.

 

Mean from frequency table Image 31 US

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

You need to use midpoints. Multiply the midpoints by the frequencies and find the total. Then divide the total by katex is not defined the frequency total.

 

Mean from frequency table Image 32.1 US

 

katex is not defined

5. The grouped frequency table shows numbers of cars at midday in a parking lot over katex is not defined days. Estimate the mean number of cars. Give your answer to the nearest tenth.

 

Mean from frequency table Image 33 US

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

You need to use midpoints. Multiply the midpoints by the frequencies and find the total. Then divide the total by katex is not defined the frequency total.

 

Mean from frequency table Image 34.1 US

 

katex is not defined

6. The grouped frequency table shows weights of katex is not defined newborn babies. Estimate the mean weight of newborn babies. Give your answer to the nearest hundredth.

 

Mean from frequency table Image 35 US

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined to  katex is not defined

GCSE Quiz False

You need to use midpoints. Multiply the midpoints by the frequencies and find the total. Then divide the total by katex is not defined the frequency total.

 

Mean from frequency table Image 36 US

 

katex is not defined

Mean from frequency table FAQs

Is a frequency table a type of graph?

While a frequency table is not a type of graph, the data that is recorded within a frequency table can be used to create graphs, including box plots, histograms, stem-and-leaf plots, dot plots, and many more.

What is the difference between grouped data and ungrouped data?

Grouped data is when the data is given in the form of class intervals, such as katex is not defined etc. Ungrouped data refers to when the data is given as individual data points or values.

What are class intervals?

Class intervals are the organized groups of the numerical data. They can have the same or different class widths, but must not overlap.

What is the standard deviation?

The standard deviation is a value that summarizes the variation around the mean. It is another measure that can be calculated from the data in frequency tables.

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