Handling Data: AVERAGES

• Learning Objective:

To be able to calculate the mode, median, range and Mean

KEY WORDS:

MEDIAN, MODE, RANGE, MEAN and AVERAGES

• All MUST be able understand how to calculate mode, median, range and Mean

• Some should be able to know which average is the best to USE!

The mean

The mean is the most commonly used average. It can only be used with numerical data.

To calculate the mean of a set of values we add together the values and divide by the total number of values.

Mean =Sum of values

Number of values

For example, the mean of 3, 6, 7, 9 and 9 is

3 + 6 + 7 + 9 + 9

5=

34

5= 6.8

Finding the mode

The mode or modal value in a set of data is the data value that appears the most often.

For example, the number of goals scored by the local football team in the last ten games is:

The modal score is 2.

Is it possible to have more than one modal value?

Is it possible to have no modal value?

Yes

Yes

2, 1, 2, 0, 0, 2, 3, 1, 2, 1.2, 1, 2, 0, 0, 2, 3, 1, 2, 1.

Finding the mode

The mode is the only average that can be used for categorical or non-numerical data.

For example, 30 pupils are asked how they usually travel to school. The results are shown in a frequency table.

What is the modal method of travel?

Method of travel Frequency

Bicycle 6

On foot 8

Car 2

Bus 6

Train 3

8Most children travel on foot.

Travelling on foot is therefore the modal method of travel.

Finding the mode from a bar chart

This bar chart shows the scores in a science test:

What was the modal score?

6 is the modal score because it has the highest bar.

0

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 9 10

Nu

mb

er o

f p

up

ils

Marks out of ten

78

2618

55

23

chocolate

fruit

vegetables

sweets

other

Finding the mode from a pie chart

This pie chart shows the favourite food of a sample of people:

What was the modal food

type?

The biggest sector of the pie chart is for chocolate, so this is the modal food type.

Finding the mode from a frequency table

This frequency table shows the frequency of different length words in a given paragraph of text.

What was the modal word length?

For this data there are two modal word lengths: 2 and 4.

We need to look for the word lengths that occur most frequently.

Word length

Frequency

1

3

2

16

3

12

4

16

5

7

6

3

7

11

8

6

9

2

10

116 16

Finding the median

The median is the middle value of a set of numbers arranged in order. For example,

Find the median of

10, 7, 9, 12, 7, 8, 6,

Write the values in order:

6, 7, 7, 8, 9, 10, 12.

The median is the middle value.

Finding the median

To find the number that is half-way between 47 and 51 we can add the two numbers together and divide by 2.

47 + 51

2=

98

2= 49

Alternatively, find the difference between 47 and 51 and add half this difference to the lower number.

51 – 47 = 4

½ of 4 = 2

2 + 47 = 49

The median of 42, 43, 47, 51, 56 and 65 is 49.

What does it mean if the range is large?

What does it mean if the range is small?

Finding the range

The range of a set of data is a measure of how the data is spread across the distribution.

To find the range we subtract the lowest value in the set from the highest value.

Range = highest value – lowest value

When the range is large it tells us that the values vary widely in size.

When the range is small it tells us that the values are similar in size.

Plenary

• Come up with ONE WORD TO describe the 3 AVERAGES and RANGE

• Mode:

• Median:

• Mean:

• Range:

Remember the three averages and range

M O D EM O D ECOOMMON

M E A NM E A NAADDD I V I D E

M E D I A NM E D I A N

MIDDDLE R A N G ER A N G E

LAARGEST

SMALLEEST

The three averages and range

There are three different types of average:

MODE

most common

MEAN

sum of valuesnumber of values

MEDIAN

middle value

The range is not an average, but tells you how the data is spread out:

RANGE

largest value – smallest value