Averages…..

In table form

We will start with discrete data

i.e. the data can only take certain values e.g. shoe size

Number of children in a car

No. of children in car Frequency (or No. of cars)

0 3

1 9

2 5

3 2

4 1

The mode means …….

most common

The mode is …….

1 child per car

The range is the

Highest number of children – smallest number (per car)

So the range =

4 – 0 = 4

It is NOT …..

9 – 1 = 8

median

Put in size order

(Already done in our table)

Find the middle value

We have 20 pieces of data

To find the position of the data value we need….

• Add 1 onto the number of data values 21

• Half this 10½

• We need to look halfway between the 10th and 11th pieces of data 1 and 1

• So the median is ……….

1

Now for the trickiest bit….

The mean

We need to find the total number of children in the cars

And then divide by the total number of cars

Add a column to your table

No. of children

Frequency

(No. of cars)

Group total

0 3 0 x 3 = 0

1 9 1 x 9 = 9

2 5 2 x 5 = 10

3 2 3 x 2 = 6

4 1 4 x 1 = 4

TOTAL 20 29

Mean number of children per car ……

Total No. of children ÷ total frequency

Mean = 29 ÷ 20 = ……..

1.45 children per car

One for you then……

No. of rings per student Frequency

0 73

1 15

2 7

3 4

4 1

Mode (most common) = …

0 rings

Range = …….

4 rings – 0 rings = 4

Median ……

• 100 pieces of data

• Do the ‘add one and half business’ which leaves us looking for the 50½ value (in between the 50th and 51st values)

• 50th value is ‘0’ and 51st value is also ‘0’

• So median is 0

Mean ……

New column on table

Like this ……

No. of rings Frequency Group Total

0 73 0 x 73 = 0

1 15 1 x 15 = 15

2 7 2 x 7 = 14

3 4 3 x 4 = 12

4 1 4 x 1 = 4

TOTAL 100 45

Mean = 45 ÷ 100 = ……

0.45

Here’s another one ……

No. of fingers Frequency

8 1

9 2

10 46

11 0

12 1

Mode = …….

10

Range = ……

12 – 8 = 4

Median

• 50 data values so do the ‘add 1 and half’ thing – we want the 25th and 26th values

• Median is 10

Mean

No. of fingers Frequency Group total

8 1 8 x 1 = 8

9 2 9 x 2 = 18

10 46 10 x 46 = 460

11 0 11 x 0 = 0

12 1 12 x 1 = 12

TOTAL 50 498

Mean =

498 ÷ 50 = 9.96