Overview: Column/Bar Graphs - CAT PDF Download

Introduction

A bar graph is a one that represents categorial data with rectangular bars with heights or lengths proportional to the value they represent. They are used to show a comparison between categories of data. They can be either vertical or horizontal. Each bar graph has a title at the top summarizing the data represented in the graph. At times, the graph may include footnotes at the bottom to explain the facts not covered in the title. One axis represents a discrete variable and the other axis represents a scale for one or two continuous variables.

Types of Bar Graphs

Simple Bar Chart

This is the most basic form of bar charts that you might have come across sometime or the other. It represents one continuous variable charted along with the one discrete variable.

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Composite Bar Chart

A composite bar graph is a way of describing information about different sub-groups of the main categories. A separate bar represents each of the subgroups and these are usually shaded differently to distinguish between them.

Deviation through Bar Chart

Deviation graphs are useful for graphical presentation of continuous variables which can have both positive and negative values, i.e. surplus or deficit, net profit or loss, net imports or exports.

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Stacked Bar Graph

Stacked Bar chart are similar to composite bar charts in the sense that they are also used to display information about the sub-groups that make up different categories. In stacked bar chart bars representing the sub-groups are placed on the top of each other to make a single column or side by side to make a single bar. The overall height or length of the bar shows the total size of the category whilst different colors or shadings are used to indicate the relative contribution of the sub-group.

Stacked bar charts are also used to show percentage contribution different sub-groups contribute to each separate category. In this case the bars representing the individual categories are all the same.

Let’s now do a couple of examples
Example 1:

(i) The ratio of the number of years, in which the foreign exchange reserves are above the average reserves, to those in which the reserves are below the average reserves is?
(a) 2:6
(b) 3:4
(c) 3:5
(d) 4:4
Ans: (c)
In this case, we first need to find the average forex reserve and then find the ratio between the years when they are above the average and below the average.
Average Forex = (2640 + 3720 + 2520 + 3360 + 3120 + 4320 + 5040 + 3120) / 8 = 3480
Now, the years that are below the average = 2000-01, 2002-03, 2003-04, 2004-05, 2007-08
The years that are above the average = 2001-02, 2005-06, 2006-07
Hence, the ratio will be 3:5

(ii) The foreign exchange reserves in 2006-07 was how many times that in 2003-04?
(a) 0.7
(b) 1.2
(c) 1.4
(d) 1.5
Ans: (d)
This one is very simple one.
Forex in 2006-07 = 5040
Forex in 2003-04 = 3360
The answer is 5040/3360 = 1.5

(iii) For each year, the percent increase of foreign exchange reserves over the previous year, is the highest?
(a) 2001-02
(b) 2002-03
(c) 2003-04
(d) 2005-06
Ans: (a)
In this question we need to use percentages,
First the years in which forex rose compared to previous year = 2001-02, 2003-04, 2005-06, 2006-07
Percentage increase in these years compared to last year, 2001-02 = (3720 – 2640)/ 2640 * 100 = 40.9090%
2003-04 = (3360 – 2520)/ 2520 *100 = 33.33%
2005-06= (4320 – 3120)/ 3120* 100 = 37.88%
2006-07 = (5040 – 4320) / 4320* 100 = 16.67%
Hence, the ans. Is 2001-02

(iv) The foreign exchange reserves in 2005-06 were approximately what percent of the average foreign exchange reserves over the period under review?
(a) 95%
(b) 110%
(c) 115 %
(d) 125%
Ans: (d)
Average forex reserve is 3480. Forex Reserve in 2005-06 = 4320.
Hence, percentage = [4320/ 3480]* 100 = 124.14% = 125%

Example 2: 

The following chart represents the number of students of AMS careers at its Lucknow center who passed either the CAT exam or XAT exam or CET exam or none of these exams. (Assume that there are no students who passed more than one exam.)

(i) What was the percentage of students who cleared CAT in 2000?
(a) 19.56%
(b) 12.65%
(c) 14.28%
(d) 11.76%
Ans: (d)
We need to calculate percentage of students who cleared CAT in 2000,
As shown above, there are 20 students who cleared CAT in 2000.
And, Total students are 170
Hence, 20/170 *100 = 11.76%

(ii) What was the percentage of students who succeeded in at least one of the three exams in 2000?
(a) 82.45%
(b) 82.8%
(c) 82.35%
(d) 83.3%
Ans: (c)
The solution is very simple,
Total students = 170
No. of students who are in none category = 30
Therefore, percentage of students who have cleared at least one = [(170 – 30) / 170] * 100 = 82.35%

(iii) Which year showed the best result in MBA entrance exam for the institute (in terms of percentage of students who cleared)?
(a) 2000
(b) 2001
(c) 2002
(d) Cannot be determined
Ans: (b)
This question again involves use of percentages. We need to find year-wise percentage of students who have cleared at least one exam.

(iv) What is the percentage increase in the no. of students in 2002 over 2000?
(a) 30%
(b) 17.64%
(c) 117.6%
(d) 85%
Ans: (b)
This is a very simple question. You can solve it on your own. The answer is 17.64%.