# Median From Frequency Tables

In these lessons, we will learn:

• how to find the median of a frequency table when the number of observations is odd.
• how to find the median of a frequency table when the number of observations is even.
• how to find the median for both discrete and grouped data.

### What Is The Median?

The median is the middle value in an ordered set of data.

In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.

If there is an odd number of observations, the median is the middle number.

If there is an even number of observations, the median will be the mean of the two central numbers.

The following table shows how to find the median from the frequency table with odd number of observations and with even number of observations. Scroll down the page for examples and step-by-step solutions.

#### How To Find The Median Of A Frequency Table When The Number Of Observations Is Odd?

Case 1. When the number of observations (n) is odd, then the median is the value at the position.

Example:
The following is a frequency table of the score obtained in a mathematics quiz. Find the median score.

 Score Frequency 0 1 2 3 4 3 4 7 6 3

Solution:
Number of scores = 3 + 4 + 7 + 6 + 3 = 23 (odd number)

Since the number of scores is odd, the median is at the position.

To find out the 12 th position, we need to add up the frequencies as shown:

 Score Frequency Position 0 1 2 3 4 3 4 7 6 3 3 3 + 4 = 7 7 + 7 =14

The 12th position is after the 7th position but before the 14th position. So, the median is 2.

#### How To Find The Median Of A Frequency Table When The Number Of Observations Is Even?

Case 2. When the number of observations (n) is even, then the median is the average of values at the n/2 and (n/2 + 1) positions.

Example:
The table is a frequency table of the scores obtained in a competition. Find the median score.

 Scores Frequency 0 1 2 3 4 11 9 5 10 15

Solution:
Number of scores = 11 + 9 + 5 + 10 + 15 = 50 (even number)

Since the number of scores is even, the median is at the average of the position and position.

To find out the 25th position and 26th position, we add up the frequencies as shown:

 Scores Frequency Position 0 1 2 3 4 11 9 5 10 15 11 11 + 9 = 20 20 + 5 = 25 25 + 10 = 35 36 to 50

The score at the 25th position is 2 and the score at the 26th position is 3.

The median is the average of the scores at 25th and 26th positions =

#### How To Find The Median From A Frequency Table (n is even)?

How to find the Mean, Median and Mode from a frequency distribution table?

Example:
The one hundred families in a particular neighborhood are asked their annual household income, to the nearest \$5 thousand dollars. The results are summarized in a frequency table. Find the median household income.

#### How To Estimate The Median, Quartiles From A Grouped Frequency Table Or Class Intervals?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.