# How to Find the Median from a Frequency Table

## Finding the Median from a Frequency Table

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

## How to Find the Median from a Frequency Table

Finding the median from a frequency table is easy.

### Question

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

What is the median test score?

### Step-by-Step:

# 1

Make sure the entries in the **Score** column are in numerical order. In our example, the entries are in numerical order.

# 2

Add another column onto the table, labelled **Cumulative Frequency**.

For each row of the table, add the entries in the **Frequency** column up to that row.

# 3

Find the entry in the bottom row of the **Cumulative Frequency** column. In this example, it is 11. (**Check:** You should get the same result if you add up the numbers in the **Frequency** column).

Find the middle number of this number. (See **Finding the Middle Number** in the **Top Tip**).

In this example, there are 11 numbers, so the middle number is the 6^{th}.

# 4

Find the first entry in the **Cumulative Frequency** column where this middle number (6) is first reached.

A cumulative frequency of 6 is first reached in the 3^{rd} row.

# 5

Find the entry in the **Score** column of this row. This is the median.

### Answer:

The median of the test scores is 7.

## How to Find the Median from a Frequency Table (with an Even Numbered Set)

In the example above, there were 11 numbers, an odd number. (The total number of numbers is the sum of the **Frequency** column or the last entry in the **Cumulative Frequency**).

The procedure is slightly different if there is an even number of numbers, which will be the case in the example below.

### Question

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

What is the median test score?

### Step-by-Step:

# 1

Make sure the entries in the **Scores** column are in numerical order. In our example, the entries are in numerical order.

# 2

Add another column onto the table, labelled **Cumulative Frequency**.

For each row of the table, add the entries in the **Frequency** column up to that row.

# 3

Find the entry in the bottom row of the **Cumulative Frequency** column. In this example, it is 10. (**Check:** You should get the same result if you add up the numbers in the **Frequency** column).

Find the middle number of this number. (See **Finding the Middle Number** in the **Top Tip**).

In this example, there are 10 numbers, so the middle number is the 5.5^{th}.

There is no 5.5^{th} number. It is halfway between the 5^{th} and 6^{th} numbers. Find the 5^{th} and 6^{th} number.

# 4

Find the 5^{th} number.

Find the first entry in the **Cumulative Frequency** column where 5 is first reached and read off the **Score**.

A cumulative frequency of 5 is first reached in the 2^{nd} row. This is a **Score** of 6. The 5^{th} number is 6.

# 5

Find the 6^{th} number.

Find the first entry in the **Cumulative Frequency** column where 6 is first reached and read off the **Score**.

A cumulative frequency of 6 is first reached in the 3^{rd} row. This is a **Score** of 7. The 6^{th} number is 7.

# 6

The median is the 5.5^{th} number, which is the mean of the 5^{th} number (6) and the 6^{th} number (7). Find the mean by adding the two numbers and dividing by 2.

Median = (6 + 7) ÷ 2 = 13 ÷ 2 = 6.5

### Answer:

The median of the test scores is 6.5.