Bar Graphs

A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different heights.

Imagine you just did a survey of your friends to find which kind of movie they liked best:

Comedy	Action	Romance	Drama	SciFi
**Table: Favourite Type of Movie**
4	5	6	1	4

We can show that on a bar graph like this:

It is a really good way to show relative sizes: we can see which types of movie are most liked, and which are least liked, at a glance.

We can use bar graphs to show the relative sizes of many things, such as what type of car people have, how many customers a shop has on different days and so on.

Example: Nicest Fruit

A survey of 145 people asked them “Which is the nicest fruit?”:

Fruit:	Apple	Orange	Banana	Kiwifruit	Blueberry	Grapes
People:	35	30	10	25	40	5

And here is the bar graph:

That group of people think Blueberries are the nicest.

Bar Graphs can also be Horizontal, like this:

Example: Student Grades

In a recent test, this many students got these grades:

Grade:	A	B	C	D
Students:	4	12	10	2

And here is the bar graph:

You can create graphs like that using our Data Graphs (Bar, Line, Dot, Pie, Histogram) page.

Histograms vs Bar Graphs

Histograms

Histogram: a graphical display of data using bars of different heights.

It is similar to a Bar Chart, but a histogram groups numbers into ranges .

The height of each bar shows how many fall into each range.

And you decide what ranges to use!

Example: Height of Orange Trees

You measure the height of every tree in the orchard in centimetres (cm)

The heights vary from 100 cm to 340 cm

You decide to put the results into groups of 50 cm:

The 100 to just below 150 cm range,
The 150 to just below 200 cm range,
etc…

So a tree that is 260 cm tall is added to the “250-300” range.

And here is the result:

You can see (for example) that there are 30 trees from 150 cm to just below 200 cm tall

(PS: you can create graphs like that using Make your own Histogram)

Notice that the horizontal axis is continuous like a number line: histogram x axis

Example: How much is that puppy growing?

Each month you measure how much weight your pup has gained and get these results:

0.5, 0.5, 0.3, −0.2, 1.6, 0, 0.1, 0.1, 0.6, 0.4

They vary from −0.2 (the pup lost weight that month) to 1.6

Put in order from lowest to highest weight gain:

−0.2, 0, 0.1, 0.1, 0.3, 0.4, 0.5, 0.5, 0.6, 1.6

You decide to put the results into groups of 0.5:

The −0.5 to just below 0 range,
The 0 to just below 0.5 range,
etc…

And here is the result:

(There are no values from 1 to just below 1.5, but we still show the space.)

The range of each bar is also called the Class Interval

In the example above each class interval is 0.5

Histograms are a great way to show results of continuous data, such as:

weight
height
how much time
etc.

But when the data is in categories (such as Country or Favourite Movie), we should use a Bar Chart.

Frequency Histogram

A Frequency Histogram is a special graph that uses vertical columns to show frequencies (how many times each score occurs):

Here I have added up how often 1 occurs (2 times),
how often 2 occurs (5 times), etc,
and shown them as a histogram.

Bar Graphs are good when your data is in categories (such as “Comedy”, “Drama”, etc).

But when you have continuous data (such as a person’s height) then use a Histogram.

It is best to leave gaps between the bars of a Bar Graph, so it doesn’t look like a Histogram.

Pie Chart

Pie Chart: a special chart that uses “pie slices” to show relative sizes of data.

Imagine you survey your friends to find the kind of movie they like best:

Comedy	Action	Romance	Drama	SciFi
**Table: Favourite Type of Movie**
4	5	6	1	4

You can show the data by this Pie Chart:

It is a really good way to show relative sizes: it is easy to see which movie types are most liked, and which are least liked, at a glance.

You can create graphs like that using our Data Graphs (Bar, Line and Pie) page.

Or you can make them yourself …

How to Make Them Yourself

First, put your data into a table (like above), then add up all the values to get a total:

Comedy	Action	Romance	Drama	SciFi	TOTAL
**Table: Favourite Type of Movie**
4	5	6	1	4	20

Next, divide each value by the total and multiply by 100 to get a percent:

Comedy	Action	Romance	Drama	SciFi	TOTAL
4	5	6	1	4	20
4/20 = 20%	5/20 = 25%	6/20 = 30%	1/20 = 5%	4/20 = 20%	100%

Now to figure out how many degrees for each “pie slice” (correctly called a sector).

A Full Circle has 360 degrees, so we do this calculation:

Comedy	Action	Romance	Drama	SciFi	TOTAL
4	5	6	1	4	20
20%	25%	30%	5%	20%	100%
4/20 × 360° = 72°	5/20 × 360° = 90°	6/20 × 360° = 108°	1/20 × 360° = 18°	4/20 × 360° = 72°	360°

Now you are ready to start drawing!

Draw a circle.

Then use your protractor to measure the degrees of each sector.

Here I show the first sector …

Finish up by colouring each sector and giving it a label like “Comedy: 4 (20%)“, etc.

(And don’t forget a title!)

Another Example

You can use pie charts to show the relative sizes of many things, such as:

what type of car people have,
how many customers a shop has on different days and so on.
how popular are different breeds of dogs

Example: Student Grades

Here is how many students got each grade in the recent test:

A	B	C	D
4	12	10	2

And here is the pie chart:

Example: 1) 40 children of a class were asked to vote for their preference
for one of the five core subjects taught in their school, the result were as follows

Subjects	English	Mathematics	Science	Sanskrit	Social Science
No.of students	6	10	9	7	8

Solution:-

Subjects	No. of students	Central angle= Value of the component / Total value X 360 degree
English	6	Central angle=6/40 X 360 = 54 degree
Mathematics	10	Central angle=10/40 X 360 = 90 degree
Science	9	Central angle=9/40 X 360 = 81 degree
Sanskrit	7	Central angle=7/40 X 360 = 63 degree
Social Science	8	Central angle=8/40 X 360 = 72 degree

Exercise 5.4: 1) Favourite outdoor of students are listed below.
Draw a pie chart for the same .

Outdoor Games	Basketball	Cricket	Hockey	Football	Volleyball
No.of students	120	180	60	150	90

Solution:-	Total Number of students = 600

Subjects	No. of students	Central angle= Value of the component / Total value X 360 degree
Basketball	120	Central angle=120/600 X 360 = 72 degree
Cricket	180	Central angle=180/600 X 360 = 108 degree
Hockey	60	Central angle=60/600 X 360 = 36 degree
Football	150	Central angle=150/600 X 360 = 90 degree
Volleyball	90	Central angle=90/600 X 360 = 54 degree

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8th Data Handling Chapter