MAL-001 –

BAR GRAPHS

AND PIE CHARTS

1 Bar charts

MAL-001 STATISTICS

Representing and interpreting data

2 Pie charts

Bar Charts and Pie Charts

Bar Chart : A graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length of height of each bar represents the frequency or percentage of observations or some other measure associated with the category. The bars may be vertical or horizontal. The bars may all be the same color or they may be different colors depicting different categories. Additionally multiple variables can be graphed on the same bar chart.

Constructing Bar Charts

1. Define the categories for the variable of interest.

2. For each category, determine the appropriate measure or value.

3. For a column bar chart, locate the categories on the horizontal axis. The vertical axis is set to a scale corresponding to the values in the categories. For a horizontal bar chart, place the categories on the vertical axis and set the scale of the horizontal axis in accordance with values in the categories. Then construct bars, either vertical or horizontal, for each category such that the length or height corresponds to the value for the category.

Bar charts for categorical data

Bar charts can be used to display categorical or non-numerical data.

For example, this bar graph shows how a group of children travel to school.

How children travel to school

0

2

4

6

8

10

12

walk train car bicycle bus other

Method of travel

Num

ber

of c

hild

ren

Bar charts for discrete data

Bar charts can be used to display discrete numerical data.

For example, this bar graph shows the number of CDs bought by a group of children in a given month.

Number of CDs bought in a month

0

5

10

15

20

25

0 1 2 3 4 5

Number of CDs bought

Num

ber

of c

hild

ren

Bar charts for two sets of data

Two or more sets of data can be shown on a bar chart.

For example, this bar chart shows favourite subjects for a group of boys and girls.

Girls' and boys' favourite subjects

0

1

2

3

4

5

6

7

8

Maths Science English History PE

Favourite subject

Nu

mb

er

of

pu

pil

s

Girls

Boys

Department: GS -YUC

Campus: Male and Female CombinedPercent of Passing and Failing Rate By Course

                       

Note: Result only shows courses that are being offered in both campuses

MATH 001

MATH 002

MATH 111

MATH 101

MATH 112

MATH 102

MATH 203

MATH 201

MATH 204

STAT 2

11

STAT 3

11

STAT 3

01

PHSC 001

PHSC 101

PHYS101

PHYS102

CSE 252

Averag

e0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

41 44

81

62

79 78 8092

8085

76

62

84

60

40

70

59 56

19

38

21 22 208

2015

24

38

16

40

60

30

Pass Fail

Drawing bar charts

When drawing bar chart remember:

Give the bar chart a title.

Label both the axes.

Use equal intervals on the axes.

Leave a gap between each bar.

Bar graph

Twenty four students of the class were asked the name of their favorite subject. The results are shown in the following table. Represent the given data on the bar graph

Favorite subject

Math Science Arabic English Islam

Number of students

7 4 4 3 7

maths science arabic english islam0

1

2

3

4

5

6

7

8

Drawing bar charts

Q.1 Use the data in the frequency table to complete a bar chart showing the number of children absent from school from each year group on a particular day.

Year Number of absences

7 74

8 53

9 32

10 11

11 10

Exercises1. Two hundred students of a school were asked to name their favorite

color so as to decide upon what should be the color of their school building. The results are shown in the table. Represent the data on bar graph.

From the bar graph answer the following questions.a. Which is the most preferred color and which is the least preferred?b. How many students have chosen white as their favorite color?

Favorite color Pink Gray Blue White Off-white

Number of Students 43 19 55 49 34

2. A test was conducted on water resistant watches made by different companies. Each of these companies claimed that their watches were water resistant . After the test the results were as shown in the graph. Write the data in tabular form. Which company has better watches?

Company A Company B Company C Company D0

50

100

150

200

250

300

Number of watches that leaked

Number of watches that leaked

2. Pie charts

Representing and interpreting data

Pie Chart A graph in the shape of a circle. The circle is divided into “slices” corresponding to the categories or classes to the displayed. The size of each slice is proportional to the magnitude of the displayed variable associated with each category or class.

Constructing Pie Charts:

1. Define the categories for the variable of interest.2. For each category, determine the appropriate measure or

value. The value assigned to each category is the proportion the category is to the total for all categories.

3. Construct the pie chart by displaying one slice for each category that is proportional in size to the proportion the category value is to the total of all categories.

FURBLES PIE CHART

PIE CHART AND BAR GRAPH

Pie charts

A pie chart is a circle divided up into sectors which are representative of the data.

In a pie chart, each category is shown as a fraction of the circle.

For example, in a survey half the people asked drove to work, a quarter walked and a quarter went by bus.

Methods of travel to work

Car

Walk

Bus

Pie charts

This pie chart shows the distribution of drinks sold in a cafeteria on a particular day.

Altogether 300 drinks were sold.

Estimate the number of each type of drink sold.

Coffee: 75

Soft drinks: 50

Tea: 175

Drinks sold in a cafeteria

coffeesoft drinkstea

Pie charts

These two pie charts compare the proportions of boys and girls in two classes.

Mr Humphry's class

Number ofboys

Number ofgirls

Mrs Payne's class

Number ofboys

Number ofgirls

Dawn says, “There are more girls in Mrs Payne’s class than in Mr Humphry’s class.” Is she right?

Drawing pie charts

To draw a pie chart you need a compass and a protractor.

The first step is to work out the angle needed to represent each category in the pie chart.

This is done by working out what fraction of the total we want to represent and multiply it by 360 degrees.

Drawing pie charts

For example, 30 people were asked which newspapers they read regularly.

The results were :

Newspaper Number of people

The Guardian 8

Daily Mirror 7

The Times 3

The Sun 6

Daily Express 6

Drawing pie charts

Method:

Write each category as a fraction of the whole and find this fraction of 360º.

8 out of the 30 people in the survey read The Guardian so to work out the size of the sector we calculate

830

× 360º = 96º

7 out of the 30 people in the survey read the Daily Mirror so to work out the size of the sector we calculate

730

× 360º = 84º

AngleWorkingNo of peopleNewspaper

6Daily Express

6The Sun

3The Times

7Daily Mirror

8The Guardian

Total

Drawing pie charts

These calculations can be written into the table.

96º

84º

36º

72º

72º

30 360º

× 360º830

× 360º730

× 360º330

× 360º630

× 360º630

Drawing pie charts

Once the angles have been calculated you can draw the pie chart.

Start by drawing a circle using a compass.

Draw a radius.

Measure an angle of 96º from the radius using a protractor and label the sector.

96º

The Guardian

Measure an angle of 84º from the the last line you drew and label the sector.

84ºThe Daily

Mirror

Repeat for each sector until the pie chart is complete.

36º

The Times

72º

72º

The Sun

The Daily Express

Drawing pie charts

Q.1 Use the data in the frequency table to complete the pie chart showing the favourite colours of a sample of people.

No of people

10

3

14

5

4

Favourite colour

Red

Yellow

Blue

Green

Purple

Total 36

Red 10

Purple 4

Green 5

Blue 14

Yellow 3

Favourite colour

Drawing pie charts

Q.2 Use the data in the frequency table to complete the pie chart showing the holiday destinations of a sample of people.

Holiday destination

No of people

UK 74

Europe 53

America 32

Asia 11

Other 10

Total 180

74

53

32

1110

Holiday destinations

UKEuropeAmericaAsiaOther

Reading pie charts

Q.3 The following pie chart shows the favourite crisp flavours of 72 children.

35º

Smokeybacon

135º Ready salted

50º

Cheese and

onion

85º

55ºSalt and vinegar

Prawn cocktail

How many children preferred ready salted crisps?

The proportion of children who preferred ready salted is:

135

360= 0.375

The number of children who preferred ready salted is:

0.375 × 72 = 27