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.
StepbyStep:
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 x_{i}, where i = 1, 2... n. n is how many numbers there are. We have x_{1}, x_{2}, ... going up to x_{n}.

Each value x_{i} occurs with a frequency f_{i}. We have f_{1}, f_{2}, ... going up to f_{n}.

f_{i}x_{i} is the product of each x_{i} with each f_{i}. We have f_{1}x_{1}, f_{2}x_{2}, ... going up to f_{n}x_{n}.

Σf_{i} is the sum of each f_{i} in the column. Σf_{i} = f_{1} + f_{2} + ... + f_{n}.

Σf_{i}x_{i} is the sum of each f_{i}x_{i} in the column. Σf_{i}x_{i} = f_{1}x_{1} + f_{2}x_{2} + ... + f_{n}x_{n}.
The formula for finding the mean, x̄ (said "x bar") is shown below:
Don't forget: The x_{i}'s and f_{i}'s stand in for numbers.
In our example above, x_{1} = 5, f_{1} = 2, x_{2} = 6, f_{2} = 3 etc.
Σf_{i} = 11 and Σf_{i}x_{i} = 77. We can calculate the mean, x̄:
x̄ = Σf_{i}x_{i} / Σf_{i} = 77 ÷ 11 = 7