# Bar Graph

Bar graphs are used to display data in a similar way to line graphs. However, rather than using a point on a plane to define a value, a bar graph uses a horizontal or vertical rectangular bar that levels off at the appropriate level.

There are many characteristics of bar graphs that make them useful. Some of these are that:

- They make comparisons between different variables very easy to see.
- They clearly show trends in data, meaning that they show how one variable is affected as the other rises or falls.
- Given one variable, the value of the other can be easily determined.

A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. This type of display allows us to:

Compare groups of data, and Make generalizations about the data quickly.

An example of a bar graph is given below :

Above graph shows the number of questions asked from different math chapters in last few years?

In Exam you will be given a bar graph like the above one and asked to answer questions like

Q1. In which year maximum number of questions was asked from Algebra?

Q2. In 2003 which chapter contributed maximum number of questions?

Q3. What is the total number of questions asked from Geometry chapter in the given period of time?

Q4. What is the percentage contribution of others in year 2004?

Lets discuss all the above questions one by one.

From the above graph its can be easily found that the number of algebra questions asked during the given time period are 10, 8, 6, 12, 9. So the maximum number of questions asked in a year is 12 and that was done in year 2005.

In year 2003 the number of questions asked from different chapters are 8, 8, 12 and 2. So highest numbers of questions were asked from Number System. Similarly try to answer the other two questions.

__Analysis of the Bar Graph__

Now let's look at the components of a bar graph individually. There is a lot of information in this section so you may wish to jot down some short notes to yourself.

** Graph Title : **The graph title gives an overview of the information being presented in the graph. The title is given at the top of the graph. In the above example Mathematics pattern in CAT is the graph titile.

** Axes and their labels: **Each graph has two axes. The axes labels tell us what information is presented on each axis. One axis represents data groups, the other represents the amounts or frequency of data groups.

** Grouped Data Axis: **The grouped data axis is always at the base of the bars. This axis displays the type of data being graphed. In our example year is represented in X axis and itâ€™s the grouped data axis

** Frequency Data Axis: **The frequency axis has a scale that is a measure of the frequency or amounts of the different data groups. Ex: Number of questions in above graph

** Bars: **The bars are rectangular blocks that can have their base at either vertical axis or horizontal axis (as in this example). Each bar represents the data for one of the data groups.

**Example 1: **

Number of Engineering Students (in hundreds) at institutions of different kinds is given in the below bar graph.

1.What was the total number of engineering students in 1989-90?

(a)28500

(b)4400

(c)4200

(d)42000

2.The growth rate in students of Govt. Engineering colleges compared to that of Private Engineering colleges between 1988-89 and 1889-90 is:

(a)more

(b)less

(c)almost equal

(d)3/2

3.The total number of Engineering students in 1991-92, assuming a 10% reduction in thenumber over the previous year, is:

(a)5700

(b)57000

(c)44800

(d)None of these

4. In 1990-91, what percent of Engineering students were studying at IITs?

(a)16

(b)15

(c)14

(d)12

Answers: 1. (d) 2. (c) 3. (d) 4. (c)

In CAT most of the questions are required to be answered from data given in two different graphs/charts. For example try to answer the question on the basis of the following charts.

If the land area under tea cultivation in Chaidesh continuously decreased in all four years from 1996 to 1999, by 10%, 7% , 4% and 1%, respectively, in which year was tea productivity (production per unit of area) the highest?

(1) 1999

(2) 1998

(3) 1997

(4) 1996

Sol.Tea productivity = Area /production

When production is maximum and area is minimum, we can say that tea productivity is the maximum. In such case, calculation of tea productivity for each of the year is not required. Area is the least in year 1999 as compared to that in the year 1996, 1997, and 1998. Also, by observation, production is maximum for year 1999. Hence tea productivity is maximum for year 1999. Choice (1)

**Example 2: **

Try to solve the following question. It is taken from CAT 1993 paper

Assets are defined as Net Fixed Assets + Net Current Assets + Investments

Q1. What is the approximate simple annual growth rate of Total Assets between 1990 and 1993 ?

a. 36%

b. 12 %

c. 9%

d. 27%

Q2. In any two consecutive years, the growth rate is lowest for:

a. Net Fixed Assets

b. Net Current Assets

c. Investments

d. Total Assets

Q3. The only item which has shown positive growth in every year between 1990 and 1993 is :

a. Net Fixed Assets

b. Net Current Assets

c. Investments

d. Total Assets

Q4. Between 1991 and 1992, the highest growth rate is seen for

a. Net Fixed Assets

b. Net Current Assets

c. Investments

d. Total Assets

**ANSWERS**

1. b. Simple Annual growth rate is (30-22)100/(22 x 3) = 12%

2. b. In any two consecutive years growth rate is lowest for Net Current Assets as it can be seen from the graph between 1991-1992

3. c.

4.c

**Example 3 : **

Study the following graph and answer questions

1. Which year shows the maximum percentage of export with respect to production?

(1)1992

(2)1993

(3)1996

(4)1995

2. The population of India in 1993 was

(1)800 million

(2)1080 million

(3)985 million

(4)900 million

3. If the area under tea production was less by 10% in 1994 than in 1993, then the approxima te rate of increase in productivity of tea in 1994 was

(1)97.22

(2)3

(3)35

(4)None of the above

4. The average proportion of tea exported to the tea produced over the period is

(1)0.87

(2)0.47

(3)0.48

(4)0.66

5. What is the first half-decadeâ€™s average per capita availability of tea?

(1)457 gm

(2)535 gm

(3)446 gm

(4)430 gm

6. In which year was the per capita availability of tea minimum?

(1)1996

(2)1994

(3)1991

(4)None of these

7. In which year was there minimum percentage of export with respect to production?

(1)1991

(2)1992

(3)1993

(4)1994

8. In which year we had maximum quantity of tea for domestic consumption?

(1)1994

(2)1991

(3)1993

(4)1996

9. What approximately was the average quantity of tea available for domestic consumption during the period?

(1)324.3 million kg

(2)400 million kg

(3)410.3 million kg

(4)320.3 million kg

10. What was approximately the average population during the period?

(1)625 million

(2)624 million

(3)600 million

(4)757 million

**ANSWERS:**

1(3)

2 (2)

3 (4)

4 (2)

5 (4)

6 (3)

7 (1)

8 (3)

9 (1)

10 (4)