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Charts, Graphs and Averages

Presented on

28 November 2008

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Charts and Graphs

Many different types of Charts and Graphs exist.You can use a variety of these to presentinformation. We will consider 5 popular types:

•Tally Chart•Pictogram•Pie Chart•Bar Chart (and Histograms)•Line Graph

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Case Study

Twenty persons were asked for their shoe sizeand the results were recorded.

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Tally Chart

Used for gathering/counting data

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Tally Chart

Shoe Size Number of Persons5

67

8

9

11

2

6

5

1

4

2

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Tally Chart

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Table summarising Shoe Size Data

Shoe Size Number of persons

5 2

6 67 5

8 1

9 4

11 2

Total 20

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Pictogram

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Pie Chart“Like a pie being sliced up”

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Pie ChartPie Chart showing Shoe Sizes for 20 persons

5 6

7 8

9 11

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Pie Chart

• Visually pleasing to the eye• Quick summary of data

• Commonly used for- Election results- Company accounts

• Does not help when comparing otherquantities outside of that Pie chart????/

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Bar Chart

0

1

2

3

4

5

6

N

u m b e r o f p e r s o n s

5 6 7 8 9 11

Shoe Sizes

Bar Chart showing Shoe Sizes for 20 persons

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Bar Chart

• Good for all sorts of comparisons• Visually appealing• Used to represent data that is in whole

numbers e.g. shoe sizes or popularity ofcelebrities

• Histograms (similar to bar charts) but used

to present data that can carry severaldecimal places e.g. time, weight, height,OR data that has been organised ingroups

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Line Graph

Line Graph showing Shoe Sizes for 20 persons

0

1

2

3

4

5

6

7

5 6 7 8 9 11

Shoe Size

N

u m b e r o f p e r s o n s

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Line Graph

•Commonly used to show rises and falls in- Share prices

- House prices- Inflation• Can be used to compare lots of information

at the same time•Less appealing to the average person

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Which Chart or Graph to use?

Depends on:

•What message you want to get across•The audience you are presenting theinformation to (what are they familiar with)

•What you prefer to use

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Activity 1

0

50

100

150

200

250

300

W e e k l y W a g e ( £ )

Dan Paul Mark Sam Joy Sue

Names of Workers

Weekly Wage of Workers in a Small Business

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Question 1

What is the total wage bill for all the workersin the business?

(a) £1,125(b) £1,100(c) £1,025

(d) £1,000

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Question 2

Which of the following is true?(a) Dan‟s wage is exactly half of Joy‟s wage

(b) Four workers have the same wage(c) Sue‟s wage is more than the total of Sam‟s and Joy‟s wages

(d) Mark earns twice as much as Dan

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Answer to Question 1

a)

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Answer to Question 2

d)

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Activity 2Pie Chart showing Election Results

Labour (45%)

Conservative (30%)

Liberal Democrat (15%)

Independent (10%)

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Question 1

30,000 people vote in an election. Theresults are shown in the pie chart above.

How many people voted for the LiberalDemocrat party?

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Answer

The number of people who voted for theLiberal Democrat Party

= 15% of 30,000= 4,500 people

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Averages

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What is an ‘Average’?

An average value is a number that istypical for a set of figures.

Four main types of averages1) Mean,2) Median,3) Mode, and4) Range

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Mean

Most commonly used average isthe Mean. Examples:

Average priceAverage wage

Average height

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How to calculate the Mean

Mean =

The total of the figures in the data set÷The number of figures in the data set

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Examples of calculating the Mean

Example 1:Calculate the mean of 2, 3, and 7.

Answer:The total of these numbers = 2 + 3 + 7 = 12

The number of figures = 3

Mean = 12 ÷ 3 = 4 So the Mean is 4

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Examples of calculating the Mean

Example 2:Calculate the mean of 16, 13, 21 and 14.

Answer: The total of these numbers =16 + 13 + 21 + 14 = 64

The number of figures = 4

Mean = 64 ÷ 4 = 16 So the Mean is 16

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Median

The figure located in the middle of a set ofdata when the numbers are arranged inascending or descending order

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Example of calculating the Median

Example 3: Find the Median of 9, 3, 5, 7, 10, 5

Answer:

Arranged in ascending order: 3, 5, 5, 7 , 9, 10

Number (s) in the middle of the list: 5 and 7

The Median is the exact middle figure, and so we need anumber half way between 5 and 7 which is 6.

So the Median is 6.

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Mode

The Mode is the most commonitem that appears in a set of data.

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Example of calculating the Mode

Example 4:Find the Mode of 6, 4, 6, 5, 3, 7, 6

Answer:Place the numbers in ascending or descendingorder. 3, 4, 5, 6, 6, 6, 7

The most common number is 6 (appears 3 times)

So the Mode is 6.

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Range

The Range is the difference between thehighest value and the lowest value in the setof numbers.

It gives us an idea about the spread of thedata.

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Further Information

• This presentation was based on variousfactsheets obtained from Skillswise athttp://www.bbc.co.uk/skillswise which is

BBC Copyright.

• There are nine factsheets under the

section „Averages - understandingaverages‟ which will enable you to learnmore.

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Activity 3