# Line Graph

In first DI chapter we discussed about Tabular Data Representation. Here we 'll try to present similar set of data in a graph. A line graph is a way to summarize how two pieces of information are related and how they vary depending on one another. The numbers along a side of the line graph are called the scale. Each variable is plotted along an axis. A line graph has a vertical axis and a horizontal axis. For example, if we wanted to graph the number of questions asked from algebra chapter in last 6 CAT editions we would have got a graph line as shown below |

X axis shows the year and the corresponding value in Y axis shows the number of questions asked in that particular year.

Now few questions can be asked on above graph

1. What was the minimum number of questions asked in any year?

2. In which year maximum number of questions was asked?

3. Between what time periods was the largest increase in number of questions?

4. Based on your observations of the graph, make a prediction about what the number of questions might be in the year 2007.

All the above questions can be answered easily except question number 4. Here the line graph is not following any particular pattern so we canâ€™t predict what will be the number of questions in year 2007.

Each type of graph has characteristics that make it useful in certain situations. Some of the strengths of line graphs are that:

- They are good at showing specific values of data, meaning that given one variable the other can easily be determined.
- They show trends in data clearly, meaning that they visibly show how one variable is affected by the other as it increases or decreases.
- They enable the viewer to make predictions about the results of data not yet recorded.

**Example 1:**

The graph below is representative of the sales, costs and tax of a certain industry Study the following graph to answer these questions:

Notes: Gross profit = Sales - Cost ; Profit = Sales - Cost - Tax

Q1. What is the tax in the year 1998 ?

a)10

b)20

c)30

d) cannot be determined

**ANSWER:** c 30

Q2. What is the % increase in gross profit from year 1997 and 2000 ?

a)250%

b)350%

c)400%

d)450%

**ANSWER:** b 250%

Q3. In 1998, the industry old 850 units. If in 1999, the price per unit increased by 50% , what was the no of units sold in 1999?

a) 550

b) 650

c) 750

d) none of these

**ANSWER:** b 650 as 850x= 170,x =0.2.after 50 % increase this becomes 0.3.So in 1999 no is 195/0.3=650

Q4. If this graph represents a kind of an index on which the industry performance can be benchmarked, and if the index started with year 1997 with a value=100, what is the average sales between years 2000,2001 and 2002 ?

a) 200

b) 208.33

c) 209.22

d) None of these

**ANSWER:** c 209.22 If in 1997 120x = 100=>, x=5/6,2000 to 2002 average sales implies (250 +225+280)/3 X 5/6 = 209.22

Q5. If in 1997, profits were 3000,what are the profits in 2002?

a)3000

b)6000

c)9000

d)12000

**ANSWER:** c 9000

__Graph Comparison __

Line graphs do not present specific data as well as tables do but line graphs are able to show relationships more clearly than tables do. Line graphs can also depict multiple series which are usually the best candidate for time series data and frequency distribution.Bar and column graphs and line graphs share a similar purpose. The column graph, however, reveals a change in magnitude, whereas the line graph is used to show a change in direction.

In summary, line graphs

1. show specific values of data well

2. reveal trends and relationships between data

3. compare trends in different groups of a variable

Now letâ€™s try one more example.

**Example 2:**

In the following line graph, Solubility - Temperature relationships for various salts is shown.

(The Y-axis denotes Solubility (kg/litres of water)

1. Which of the following salts has greatest solubility?

a) Potassium Chlorate at 800C.

b) Potassium Chloride at 350C.

c) Potassium Nitrate at 390C.

d) Sodium Chloride at 850C.

2. Approximately, how many kg of Potassium Nitrate can be dissolved in 10 litres of water

at 300C?

(a) 0.04

(b) 0.4

(c) 4

(d) 0.35

3. By what % is the solubility of Potassium Chlorate in water increased as the water is heated from 300C to 800C?

(a) 100

(b) 200

(c) 250

(d) 300

4. If 1 mole of Potassium Chloride weighs 0.7456 kg, approximately, how many moles of Potassium Chloride can be dissolved in 100 litres of water at 360C?

(a) 70

(b) 60

(c) 48

(d) 54

5. Which of the salts has greatest change in solubility in kg/litre of water between 150C and 250C?

(a) Potassium Chlorate

(b) Potassium Nitrate

(c) Sodium Chlorate

(d) Sodium Nitrate

ANSWERS are 1. (c) 2. (c) 3. (d) 4. (d) 5. (c)

**Example 3:**

Use this additional information which provides statistics about the voting population in a country and votes secured by the national party during the above mentioned election

Q1. If the population in the country in the year 1989 was 800 mn, how many million votes did the party secure in this election?

(1) 159.84

(2) 360

(3) 266.4

(4) None of these

Q2. If the population increased by 12% between the year 1984 and 1989, what was the % increase in the % of population that is eligible to vote in the election?

(1) 10.24%

(2) 12%

(3) M.64%

(4) 15.50%

Q3. Between 1996 and 1998, the number of people eligible to vote increased by 10% What was the % increase in population between 1996 and 1998?

(1) 6.28%

(2) 4.4%

(3) 3.28%

(4) Cannot be determined

Q4. If in the year 1984, if for even additional 3% of the votes polled for the party meant the party get to have 450 seats in the parliament if the overall population of the country was 800 million in that year?

(1) 52.25 mn

(2) 15.43 mn

(3) Cannot be determined

(4) None of these

Q5. Which of the following is true?

(1) The largest % of votes were polled to the above party in the 1988 election.

(2)A higher % of votes to the party in a particular election does not have a direct correlation to the number of seats won by the party in the election.

(3) In four of the election, the number of seats won by the party increased over the previous election.

(4) None of these.

**ANSWERS: ** 1. (1) 2. (4) 3. (1) 4. (4) 5. (2)