objectives 1. be able to find the mean from a frequency table. 2. be able to compare two...

Objectives

1. Be able to find the mean from a frequency table.

2. Be able to compare two distributions using the mean and

the range.

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.

ABC Motoring

That’s better!

Number of tests taken

Number of People

1 9

2 11

3 7

4 6

5 3

6 2

7 2

Finding the Mean

Number of tests taken

Number of People

1 9

2 11

3 7

4 6

5 3

6 2

7 2

Remember, when finding the mean of a set of data, we add together all the pieces of data.

This tells us that there were nine 1’s in our list. So we would do

1+1+1+1+1+1+1+1+1 = 9

It is simpler to use 1x9!!

We can do this for every row.

Finding the Mean

Number of tests taken

Number of People

1 9

2 11

3 7

4 6

5 3

6 2

7 2

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

We now need to add these together 117So we have now added all the values up. What do we do now?We divide by how many values there were.So we divide by the total number of people.

40

Finding the Mean (student sheet.)

Number of tests taken

Number of People

1 9

2

3

4

5

6

7

hhhhhhhhhh

40

Number of tests taken

Number of People

1 9

2 11

3 7

4 6

5 3

6 2

7 2

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

11740

The Mean is 117 ÷ 40 = 2.9 (1dp)

ABC Motoring

Students who learn to drive with ABC motoring, pass their driving test after a mean number of 2.9 tests.

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 …

Bob’s Driving School

Number of tests taken

Number of People

1 3

2 11

3 12

4 10

5 4

We can now find the mean

hhhhhhhhhh

1 x 3 = 3

2 x 11 = 22

3 x 12 = 36

4 x 10 = 40

5 x 4 = 2012140

The Mean is 121 ÷ 40 = 3.0 (1dp)

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.

Which Driving School?

Which of the two driving schools would you choose?

ABC Motoring

0

2

4

6

8

10

12

1 2 3 4 5 6 7

Number of tests taken

Num

ber

of s

tude

nts

Bob's Driving School

0

2

4

6

8

10

12

14

1 2 3 4 5

Number of tests taken

Num

ber

of s

tude

nts

Mean = 2.9

Range = 6

Mean = 3.0

Range = 4