How to Find the Mean from a Frequency Table

Finding the Mean from a Frequency Table

We can find the mean of a set of numbers that are presented in a frequency table.

How to Find the Mean from a Frequency Table

Finding the mean from a frequency table is easy.

Question

The frequency table below shows the test scores for a class of students.

Step-by-Step:

1

Add another column onto the table, labelled Score × Number.

For each row of the table, multiply the entry in the Score column with the entry in the Frequency column.

Enter the answer in the Scores × Frequency column.

Note: The columns have been labelled (1), (2) and (3). (3) = (1) × (2) indicates the entry in column (3) are the product of the entries in column (1) and (2).

2

Add another row at the bottom of the table, labelled Total.

Add the numbers in the Frequency column, and write the total underneath in the Total row.

2 + 3 + 2 + 2 + 1 + 1 = 11

3

Add the numbers in the Scores × Frequency column, and write the total underneath in the Total row.

10 + 18 + 14 + 16 + 9 + 10 = 77

4

Divide the total of the Scores × Frequency column (77) by the total of the Frequency column (11).

77 ÷ 11 = 7

Answer:

The mean of the test scores is 7.

A Formula to Find the Mean from a Frequency Table

There is a formula to find the mean from a frequency table.

To use it, we must introduce some formal notation.

  • Let each value be xi, where i = 1, 2... n. n is how many numbers there are. We have x1, x2, ... going up to xn.

  • Each value xi occurs with a frequency fi. We have f1, f2, ... going up to fn.

  • fixi is the product of each xi with each fi. We have f1x1, f2x2, ... going up to fnxn.

  • Σfi is the sum of each fi in the column. Σfi = f1 + f2 + ... + fn.

  • Σfixi is the sum of each fixi in the column. Σfixi = f1x1 + f2x2 + ... + fnxn.

The formula for finding the mean, (said "x bar") is shown below:

Don't forget: The xi's and fi's stand in for numbers.

In our example above, x1 = 5, f1 = 2, x2 = 6, f2 = 3 etc.

Σfi = 11 and Σfixi = 77. We can calculate the mean, :

x̄ = Σfixi / Σfi = 77 ÷ 11 = 7

Slider

The slider below gives another example of how to find the mean from a frequency table.

Open the slider in a new tab

See Also

What is the mean? What is a frequency table? What is an average? Learn more about finding the mean from a frequency table ( interactive widget)