## Line Graph – Data Interpretation for CAT

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As the name suggests, data interpretation is all about logical interpretation of the given data and answering questions. Data interpretation carries the same weightage in third section of CAT as reading comprehension in verbal section or geometry and algebra in quant section. For the past two years (CAT 2014 & CAT 2015), CAT carries approximately 20 questions on data interpretation. If you haven’t been serious about this topic till now, there is never a better day than today to start!

Data can be represented in many ways, some of the most common ways are tables, bar graphs, Line Graphs, paragraphs, pie charts etc… This article will focus on LINE GRAPHS and will introduce you with the most basic aspects of a line graph.

above is one of the basic example of a line graph and its various component are as follows:

Title : The title of the graph tells us what the graph is about

Label : Horizontal and vertical labels tell us about type of the data

Axis : X and Y axises tell us about the unit of the data.

Dots : Dots on the line graph tell us combination of X and Y axis data.

Line : The blue line connecting the dots in the above graph gives a visual representation of the data, and its variation.

Look at the graph below and check its different component.

Title : The graph is about “No of students at TathaGat centre”.

Label : Horizontal label represents “Time” and vertical label represents “No of students” .

Axis : X axis represents time in hours and Y axis represents absolute number.

Dots : Dots represents the number of boys at a particular time at TathaGat centre. i.e. there were 50 boys at 12:00’o clock at TathaGat centre.

Line : That blue line is showing how the number of students first increases from 12:00 to 13:00’o clock and then decreases to 40 at 14:00’o clock and then kept increasing till 16:00’o clock.

From the above visual representation we can easily say that when line goes up the number of students increases and when it goes down the number of student decreases. But at the same time the above blue line can also tells us the rate of this increment or decrement or in other words growth (positive or negative) of the given data.

Rate of the increment or decrement is directly related with the **slope** of the line. Slope is nothing but the **steepness** or the **inclination** of the line. Growth is directly proportional to the steepness of the line that is Steeper line represents higher growth. So far we have seen line graph with single variable or single data, below is the example of a line graph with two variable.

Observe the graph and its different component carefully and answer the question:

**Q1.** At what time the number of boys were highest at the centre?

**Q2.** At what time the total number of students were lowest at the centre?

**Q3.** During what period the rate of growth of the numbers of girls were highest?

**Lets try some more questions:**

**Set 1:**

In the below given Line graph one of the line shows the number of people who attended the rallies of different candidates in Delhi Assembly election 2015 and other line shows the number of people who actually voted for them. Assume that only whoever was present during the rally, voted for one of these candidates.

Q1. What is the ratio of number of people who were not present during Kejriwal’s rally and number of people who did not vote for him?

1. $\frac{33}{83}$ 2. $\frac{38}{79}$ 3. $\frac{41}{91}$ 4. $\frac{7}{17}$

Q2. Which of these candidate received maximum percentage of vote with respect to the number of people attended their rallies?

1. Arvind Kejriwal

2. Ajay Maken

3.Kiran Bedi

4.Others

Q3. Percentage of people who were present in the Kiran Bedi’s rally but did not vote for her is equal to

1. 38.67 %

2. 61.33 %

3. 27.27 %

4. Cannot be determined

Q4. Minimum what percent of voters who voted for Others should have voted for Kiran bedi to make her win the election?

1. 44.44%

2. 42.85%

3. 47.61%

4. 49.49%

**Set 2:**

“COLACOCA” and “SESPI” are two different finance companies and they declare fixed annual rate of interest on the amounts invested with them by investors. The annual rate of interest offered by the two Companies over the years are shown by the line graph below.

Q1. In year 2000, a part of Rs. 60 lakhs was invested in “COLACOCA” and the rest was invested in “SESPI” for one year. The total interest received was Rs. 4.86 lakhs. What was the amount invested in “COLACOCA”?

1. 18

2. 36

3. 24

4. 40

Q2. An investor invested a sum of Rs. 12 lakhs in “COLACOCA” in 1998. The total amount received after one year was re-invested in the same Company for one more year. The total appreciation received by the investor on his investment was?

1. 2,96,200

2. 2,42,200

3. 2,25,600

4. 2,16,000

Q3. An investor invested Rs. 5 lakhs in “SESPI” in 1996. After one year, the entire amount along with the interest was transferred as investment to “COLACOCA” in 1997 for one year. What amount will be received from “COLACOCA”, by the investor?

1. 5,94,550

2. 5,80,425

3. 5,77,800

4. 5,77,500

Q4. A sum of Rs. 4.75 lakhs was invested in “SESPI” in 1999 for one year. How much more interest would have been earned if the sum was invested in “COLACOCA”?

1. 19000

2. 14250

3. 11750

4. 9500

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