1. Objective Be able to find the mean from a frequency table.
Be able to compare two distributions using the mean and the range.

2. ABC Motoring
Here are the number of tests taken before successfully passing a driving test by 40 students of “ABC Motoring”
2, 4, 1, 2, 1, 3, 7, 1, 1, 2, 2, 3, 5, 3, 2, 3, 4, 1, 1, 2, 5, 1, 2, 3, 2, 6, 1, 2, 7, 5, 1, 2, 3, 6, 4, 4, 4, 3, 2, 4
It is difficult to analyse the data in this form. We can group the results into a frequency table.

3. ABC Motoring Number of tests taken Number of People 1 9 2 11 3 7 4 6 5
That’s better!

4. Finding the Mean Number of tests taken Number of People 1 9 2 11 3 7 4
Remember, when finding the mean of a set of data, we add together all the pieces of data.
Number of tests taken
Number of People 1 9 2 11 3 7 4 6 5
This tells us that there were nine 1’s in our list. So we would do
= 9
It is simpler to use 1x9!!
We can do this for every row.

5. Finding the Mean Number of tests taken Number of People 1 9 2 11 3 7 46 5
hhhhhhhhhh
1 x 9 = 9
2 x 11 = 22
3 x 7 = 21
4 x 6 = 24
5 x 3 = 15
6 x 2 = 12
7 x 2 = 14 40
107
So we have now added all the values up. What do we do now?
So we divide by the total number of people.
We divide by how many values there were.
We now need to add these together

6. The Mean is 107 ÷ 40 = 2.7 (1dp) Number of tests taken
Number of People 1 9 2 11 3 7 4 6 5
hhhhhhhhhh
1 x 9 = 9
2 x 11 = 22
3 x 7 = 21
4 x 6 = 24
5 x 3 = 15
6 x 2 = 12
7 x 2 = 14 40
107
The Mean is
107 ÷ 40 = 2.7 (1dp)

7. ABC Motoring
Students who learn to drive with ABC motoring, pass their driving test after a mean number of 2.7 tests.

8. Bob’s Driving School
Now let’s look at another Driving school from the same town. Here are the number of tests taken by 40 students at “Bob’s Driving School”
3, 2, 4, 1, 3, 2, 3, 1, 2, 1, 2, 4, 4, 4, 5, 2, 3, 4, 3, 4, 4, 5, 5, 2, 3, 2, 4, 5, 3, 3, 4, 3, 2, 2, 2, 2, 4, 3, 3, 3
Grouping the data will help us to analyse it more efficiently …

9. Bob’s Driving School The Mean is 121 ÷ 40 = 3.0 (1dp)
Number of tests taken
Number of People 1 3 2 11 12 4 10 5
hhhhhhhhhh
1 x 3 = 3
2 x 11 = 22
3 x 12 = 36
4 x 10 = 40
5 x 4 = 20 40
121
The Mean is
121 ÷ 40 = 3.0 (1dp)
We can now find the mean

10. Bob’s Driving School
Students who learn to drive with Bob’s Driving School, pass their driving test after a mean number of 3.0 tests.

11. Which Driving School?
Which of the two driving schools would you choose?

12. Mean = 2.7
Range = 6
Mean = 3.0
Range = 4