AP®StatisticsCollege BoardRevision NotesUnit 1: Exploring One-Variable Data and Collecting DataSummary StatisticsGrouped Data

Grouped Data (College Board AP® Statistics): Revision Note

Syllabus Edition

First teaching 2026

First exams 2027

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on 21 May 2026

Mean from grouped data

How do I find the mean for grouped data?

The exact mean from a set of grouped data cannot be found
- but an estimate can be calculated
To find an estimate for the mean of grouped data in a table:
- Create two new columns for the table and label them $x$ and $f x$
- Find the midpoint of each group and write it in the column labeled $x$
- Multiply the frequency of each group by the group's midpoint and write it in the column labeled $f x$
- Find the sum of these values
- Divide the sum by the total frequency
The formula to find the mean of grouped data is $\bar{x} = \frac{\sum_{} f x}{\sum_{} f}$
- This is not given to you in the exam

Examiner Tips and Tricks

If the exam contains raw data, then you should calculate the exact mean rather than grouping the data. Only estimate the mean if you are given grouped data.

Worked Example

The weights of 20 three-week-old Labrador puppies were recorded at a vet's clinic. The results are shown in the table below.

Weight, w kg	Frequency
3 ≤ w < 3.5	3
3.5 ≤ w < 4	4
4 ≤ w < 4.5	6
4.5 ≤ w < 5	5
5 ≤ w < 6	2

Estimate the mean weight of these puppies.

Answer:

Add two columns to the table and complete the first new column with the midpoints of the class intervals

Complete the second extra column by calculating $f x$

It is worth also adding a total row at the bottom of the table

Weight, w kg	Frequency	Midpoint	$f x$
3 ≤ w < 3.5	3	3.25	3 × 3.25 = 9.75
3.5 ≤ w < 4	4	3.75	4 × 3.75 = 15
4 ≤ w < 4.5	6	4.25	6 × 4.25 = 25.5
4.5 ≤ w < 5	5	4.75	5 × 4.75 = 23.75
5 ≤ w < 6	2	5.5	2 × 5.5 = 11
Total	20		85

Find the estimate of the mean by dividing the total of the $f x$ column by the total of the frequency column, $\frac{\sum_{} f x}{\sum_{} f}$

Mean $= \frac{85}{20} = 4.25$

An estimate of the mean weight of the puppies is 4.25 kg

Median from grouped data

How do I find the median for grouped data?

The exact median from a set of grouped data cannot be found
- but the group that contains the median can be identified
The position of the median can be found using $\frac{n + 1}{2}$
- where $n$ is the total number of data values (total frequency)
For grouped data in a table
- Find the interval containing the ${(\frac{n + 1}{2})}^{th}$ value (median)
- You could add another column to the table containing the cumulative frequency to help you find this
  - This is a column that adds up the frequency as you go along

Worked Example

The heights of 30 mature oak trees were measured and recorded in the table below.

Height, h m	Frequency
22 ≤ h < 23	4
23 ≤ h < 24	7
24 ≤ h < 25	6
25 ≤ h < 26	8
26 ≤ h < 27	3
27 ≤ h < 28	2

Find the height interval that contains the median height of the mature oak trees.

Answer:

Calculate the position of the median within the data set

$\frac{30 + 1}{2} = 15.5$

This means that the median lies between the 15th and 16th data values

Add a 'cumulative frequency' column to the table to add up the frequency as you go along

Height, h m	Frequency	Cumulative frequency
22 ≤ h < 23	4	4
23 ≤ h < 24	7	11
24 ≤ h < 25	6	17
25 ≤ h < 26	8	25
26 ≤ h < 27	3	28
27 ≤ h < 28	2	30

Identify the group(s) that contain the 15th and 16th values

Both the 15th and 16th values are in the group 24 ≤ h < 25

Therefore the median must also lie in this group

The median height of the mature oak trees lies in the interval 24 ≤ h < 25, where h is the height in meters

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Grouped Data (College Board AP® Statistics): Revision Note

Mean from grouped data

How do I find the mean for grouped data?

Examiner Tips and Tricks

Worked Example

Median from grouped data

How do I find the median for grouped data?

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Naomi C

Reviewer: Dan Finlay