Finding the Mean from Frequency Tables

In your maths exam you will probably get asked to find or estimate the mean from a frequency table.  It is a 3 or 4 mark question and really easy marks if you can remember the method correctly.  It is nearly always on your calculator paper.
Interactive worksheets:
Practice GCSE questions:

Example Question

The table below shows the selling price of 52 cars in a second hand showroom.
Price (£x) Frequency
0 < x ≤ 2500
2500 < x ≤ 5000
5000 < x ≤ 7500
7500 < x ≤ 10000
10000 < x ≤ 12500		 9
13
21
7
2

Calculate an estimate of the mean selling price.  Give your answer to the nearest pound.

Solution
The first thing to note is that the question says "estimate".  This is because the data is grouped so we don't know the exact selling price of each car.  Instead we estimate that each car was sold for the value in the middle of its grouping.  E.g £1250, £7250 etc.  If the data is not grouped you don't have to do this!

In your exam the table will normally be written to the left hand side of the page.  This is so you can add two extra columns to the table, one for "mid point" and one for "frequency x mid point".  Remember you don't need a midpoint column if the data isn't grouped!
Price (£x) Frequency Mid Pt. Freq x Mid Pt
0 < x ≤ 2500
2500 < x ≤ 5000
5000 < x ≤ 7500
7500 < x ≤ 10000
10000 < x ≤ 12500		 9
13
21
7
2		 1250
3750
6250
8750
11250		 11250
48750
131250
61250
22500
Total = 52 Total = 275000

The mid point values are the middle numbers in each of the groups.  An easy way to find these is to add the upper and lower boundary and divide your answer by two.

The last column is found by multiplying the mid point by the frequency.  E.g. 1250 x 9 = 11250.

Finally, to get our answer we add up the Frequency x Mid Point column and divide it by the total frequency.
275000 = 5288.461538
52                        
                         = £5288 (nearest £)

To check our answer is sensible we make sure that our average price is between £0 and £12500.  Otherwise we know we have made a mistake somewhere!
Test Yourself!
The table below shows the number of pets owned by 40 families.
Number of Pets Frequency
0
1
2
3
4		 13
14
8
3
2

Calculate an estimate of the mean number of pets.  Give your answer to one decimal place.



 

The table below shows the scores of 26 students in a maths test.
Score (x%) Frequency
0 < x ≤ 20
20 < x ≤ 40
40 < x ≤ 60
60 < x ≤ 80
80 < x ≤ 100		 1
4
8
11
2

Calculate an estimate of the mean score.  Give your answer to the nearest percent.
%

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