*Tuesday, February 19th, 2019*

Data Interpretation section of CAT revolves around decoding the structured data and deriving meaningful results from the given data. Its significance cannot be undermined in todayâ€™s world as strategies are planned and implemented on the basis of inferences and results determined through this vast amount of data. Thus, this topic holds an inevitable place in CAT exam and around 16 questions are asked from it. The data can be represented in form of lines, graphs or charts, tables, and caselets etc. And, in this blog, we will be talking about one special kind of graph known as bar graphs. But before moving forth with understanding bar graphs you should also possess the knowledge of basic arithmetic calculations such as division, multiplications, ratio and proportion, percentages etc. as the questions that will be asked in the exam will involve the use of this mathematical accounting.

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**

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.

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 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.

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.

Letâ€™s now do a couple of examples

**Ques 1:** 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

**Ques 2:** 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

**Ques 3:** 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

**Ques 4:** 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%

**Solution:** As you can clearly notice that all the questions asked above involves simple mathematic calculations and use of concepts such as averages, ratios, percentages etc. You just need to understand the data given in the graph and find the solution to the questions asked hereafter.

**Ans 1:** 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**

**Ans 2:** This one is very simple one.

**Forex in 2006-07 **= 5040

**Forex in 2003-04 **= 3360

The answer is 5040/3360 = 1.5

**Ans 3:** 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 â€“ 2640)/ 2640 * 100 = 40.9090%

**2003-04 = **(3360 â€“ 2520)/ 2520 *100 = 33.33%

**2005-06**= (4320 â€“ 3120)/ 3120* 100 = 37.88%

**2006-07** = (5040 â€“ 4320) / 4320* 100 = 16.67%

Hence, the ans. Is 2001-02

**Ans 4:** 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.)

**Ques 1:** What was the percentage of students who cleared CAT in 2000?

a.) 19.56%

b.) 12.65%

c.) 14.28%

d.) 11.76%

**Ques 2:** 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%

**Ques 3:** 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

**Ques 4:** What is the percentage increase in the no. of students in 2002 over 2000?

a.) 30%

b.) 17.64%

c.) 117.6%

d.) 85%

**Sol:** Again, these questions have to be solved in the similar way like the earlier ones, the only difference is that the here stacked bar graph is used with sub-categories as CAT, XAT, CET and none unlike the simple bar graph we had in the first example.

**Ans 1:** 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%**

**Ans 2:** 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 â€“ 30) / 170] * 100 = 82.35%

**Ans 3:** This question again involves use of percentages. We need to find year-wise percentage of students who have cleared at least one exam.

Year |
% od students who have cleared at least one exam |

2000 |
82.35 |

2001 |
[(180 â€“ 30) * 100]/ 180 = 83.33% |

2002 |
[(200 â€“ 40) * 100]/ 200 = 80 |

Using the table, we get the answer 2001.

**Ans 4:** This is a very simple question. You can solve it on your own. The answer is 17.64%.

**Example 3:**

*The total of first three deficit countries is = 3594.3. The total of next five deficit countries is = 2588.5. The total of last five deficit counties is = 334.2

**Ques 1:** The ratio between the difference between the highest and the lowest of the surplus countries to the difference between Bangladesh and Oman?

a.) 3.44

b.) 2.96

c.) 4.5

d.) 3.83

**Ques 2:** The average of the total deficit of the middle 5 deficit is closest to the deficit of which country?

a.) Korea

b.) South Africa

c.) UAE

d.) None of these

**Ques 3:** The state whose surplus is nearly equal to the average of the four surplus countries is

a.) Sri Lanka

b.) UAE

c.) USA

d.) UK

**Ques 4:** The net total deficit/surplus is equal to?

a.) 4666.6 surplus

b.) 4666.6 deficit

c.) 3836.5 deficit

d.) None of these

**Sol:** This question belongs to the deviation category. In this one, various countries along with their surplus and deficit are provided. Here, values above x axis are positive values and below are the negative ones. Letâ€™s solve it.

**Ans 1:** We need to calculate the ratio between the difference here,

Highest and lowest surpluses are of UK and Sri Lanka respectively. The difference between them is 359.3

The difference between the deficit of Bangladesh and Oman is 94.7

**Hence, the required ratio is 349.3: 93.7 = 3.8264**

**Ans 2:** We need to use the average in this question,

The middle five deficit countries are India, New Zealand, South Africa, Korea, Namibia.

Their average is 1946.6/ 5 = 389.32, which is closest to Korea.

**Ans 3:** This question is similar to the above one. It just now wants to calculate surplus and find the nearest countries that matches with it. The answer is USA

**Ans 4:** The net deficit/ surplus is

**Total surplus â€“ Total deficit = 1850.4 â€“ 6517 = 4666.6**

**XAT 2011: **Five years ago, Maxam Glass Co., had estimated its staff requirement in the five levels in their organization as:

Level 1: 55; Level 2: 65; Level 3: 225; Level 4: 225; & Level 5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defense service men and policemen. The following graph shows actual strength at various levels as on date.

**Question 1:** The level in which the Ex-defence servicemen are highest in the percentage terms is

a.) 1

b.) 2

c.) 3

d.) 4

e.) 5

**Question 2:** If the company decides to abolish all vacant posts at all the levels, which level would incur the highest reduction in percentage terms?

a.) 1

b.) 2

c.) 3

d.) 4

e.) 5

**Question 3:** Among all the levels, which level has the lowest representation of Ex-policemen?

a.) 1

b.) 2

c.) 3

d.) 4

e.) 5

**Sol:** I will provide the solution to first two questions, solve the last one yourself itâ€™s an easy one

1.)Â We need to find level-wise percentage of Ex-defence servicemen.

Levels |
Percentage of Ex-defence servicemen |

1 |
9.67% |

2 |
10.38% |

3 |
12.04% |

4 |
15.43% |

5 |
14.81% |

**Clearly, the answer is Level 4**.

2.) Again, this question involves the use of percentages. We need to evaluate the reduction in staff in percentage terms as compared to the prescribed requirement stated in the question.

Level |
Requirement |
Excess/ deficit |
Percentage term |

1 |
55 | 7 | 12.72% |

2 |
65 | 12 | 18.46% |

3 |
225 | 24 | 10.667% |

4 |
225 | -63 | -28% |

5 |
300 | 105 | 35% |

**Hence, the solution is Level 5.**

**CAT2010**: Study the following bar graph and line graph giving the details of â€˜Number of Workers Employedâ€™ and â€˜Number of Units Shippedâ€™ respectively of M/s Mega Corp Ltd. To answer these questions.

**Question 1:** By what percent did the number of temporary workers employed by M/s Mega Corp Ltd. Increase from Apr 1 to May 1?

a.) 40%

b.) 25%

c.) 20%

d.) 12%

**Question 2:** What was the difference, if any, between the number of permanent workers employed by M/s Mega Corp led. On March 1 and the number of permanent workers employed on April 1?

a.) 0

b.) 50

c.) 100

d.) 150

**Question 3:** If on May 1, 60% of the permanent workers and 40% of temporary workers employed by M/s Mega Corp Ltd. were women, how many of the workers employed by M/s Mega Corp Ltd. at the time were women?

a.) 200

b.) 120

c.) 410

d.) 260

**Sol: **1. Temporary workers as on Apr 1: 250

Temporary workers as on May 1: 350

**% increase: 100/250 * 100 = 40%**

- This is a very basic question and the answer is 50
- Permanent workers as on May 1: 450

Women workers on May 1: 60% of 450 = 270

Temporary workers as on May 1: 350

Women workers on May 1: 40% of 350 = 140

**Total no of women = 410.**

As you can notice in the above questions that solving Data Interpretation sets on bar graphs are so simple and requires very basic arithmetic calculations. They just involve use of the given data illustrated in bar graphs in basic mathematical operations such as addition, subtraction, division etc. In exam, you can get questions based on composite bar graphs or you can get two simple bar graphs or some other combination of two types of them to confuse students. But thereâ€™s no major difference in them and the questions you solved above. The key is understanding what the graph is illustrating and you are done. Try practicing a few different questions so that no such confusions and surprises happens at the time of exam.

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