Mode & Mean from Grouped Data (Edexcel GCSE Statistics)
Revision Note
Written by: Roger B
Reviewed by: Dan Finlay
Mode & Mean from Grouped Data
How do I estimate the mean for grouped data?
It is impossible to find the mean for grouped data, because we don't have access to the original data values
i.e. there is no way to find the exact sum of all the data values
so we can't use the formula
However we can estimate the mean for grouped data
To do this we use the class midpoints as our data values
e.g. if a class interval is 150 ≤ x < 160
we assume that all the data values are equal to the midpoint, 155
STEP 1
Draw an extra two columns on the end of a table of the grouped dataIn the first new column write down the midpoint of each class interval
If the midpoint isn't obvious, add the endpoints and divide by 2
e.g. if a class interval is 150 ≤ x < 160
the midpoint is
STEP 2
Calculate "frequency" × "midpoint" (this is often called fx)Write these values in the second column you added to the table
STEP 3
Total the fx column and (if necessary) the frequency columnThe question may already tell you the total number of data values (i.e. the total frequency)
In that case there's no need to find the total of the frequency column
STEP 4
Estimate the mean by using the formulai.e. divide the total of the fx column by the total number of data values
How do I find the modal class?
It is impossible to find the modal value (i.e. mode) for grouped data, because we don't have access to the original data values
i.e. it is impossible to say which value occurs the most times
For grouped data we talk about the modal class instead
This is the class with the highest frequency
Just find the highest frequency in the table
The corresponding class interval tells you the modal class
Be careful not to confuse the modal class with its frequency
e.g. if the highest frequency in the table is 34, corresponding to the class interval
then the modal class is
The modal class is not '34'!
What if the grouped data is in a histogram?
Remember that a histogram is a way of presenting grouped data as a diagram
The modal class will be the one with the highest bar on the histogram
To estimate the mean it will usually be easiest to rewrite the data as a table first
The class intervals can be read off the horizontal axis
The frequencies can be read off the vertical axis
Examiner Tips and Tricks
When presented with data in a table it may not be obvious whether the data is grouped or not
When you see the phrase “estimate the mean” you know that you are in the world of grouped data!
So use the midpoint technique to answer the question
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 | 2 |
3.5 ≤ w < 4 | 4 |
4 ≤ w < 4.5 | 6 |
4.5 ≤ w < 5 | 5 |
5 ≤ w < 5.5 | 2 |
5.5 ≤ w < 6 | 1 |
(a) Estimate the mean weight of these puppies.
First add two columns to the table
Complete the first new column with the midpoints of the class intervals
Complete the second extra column by calculating "fx"
A total row is also useful
Weight, w kg | Frequency | Midpoint | "fx" |
3 ≤ w < 3.5 | 2 | 3.25 | 2 × 3.25 = 6.5 |
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 < 5.5 | 2 | 5.25 | 2 × 5.5 = 10.5 |
5.5 ≤ w < 6 | 1 | 5.75 | 1 × 5.75 = 5.75 |
Total | 20 |
| 87 |
Now we can find the mean using
4.35 kg
(b) Write down the modal class.
The highest frequency in the table is 6
This corresponds to the interval 4 ≤ w < 4.5
4 ≤ w < 4.5
A common error here would be to write down 6 (the frequency) as the modal class
Last updated:
You've read 0 of your 10 free revision notes
Unlock more, it's free!
Did this page help you?