Line graph is also known as line chart. It is one of the most common graphs which is used almost in every field. Line graph is a graph in which points belonging to an observation are plotted on X-Y plane and every two consecutive points are joined together using a straight line. Line graph is named so, because a line is used to represent the data. An example of line graph is given below: Sales of a particular organization in different years.

Line graph is often used to visualize rate of change of a quantity. It is more useful when the given data has peaks and valleys. Line graphs are very simple to draw and quite convenient to interpret.

## Line Graph Data

The data used in line graph is generally a sample data. Line graph is drawn between two sets of variables one of which is represented on X axis and other on Y axis. One variable is independent variable and usually marked at X axis, while other variable is dependent variable and usually marked at Y axis. The independent variable is generally a qualitative variable in line graph data (Though, It is not mandatory).
Line graph is preferred when rate of change of quantity is observed.
Few examples of the types of data used in line graph are as follows:
• Speed and time
• Sales and expenditure
• Year and production
• Days and number of an article sold
• Months and household expenditure
• States and their population
• City and temperature
• Height and weight
• Age and weight

## Parts of a Line Graph

Following figure demonstrates the parts of a line graph:

Parts mentioned above are discussed as follows:
1. Horizontal axis or X axis: Line graph has one horizontal axis which is called X axis. It represents independent variables.
2. Vertical axis or Y axis: Line graph has one vertical axis which is called Y axis and is exactly perpendicular to X axis. It represents dependent variables.
3. Origin: The point where X axis and Y axis meet is called origin. In the above figure, O is the origin.
4. Labels: Each axis has to be given a label explaining which variable it is representing.
5. Data Points: In line graph, points are plotted corresponding to X axis and Y axis. These points are called data points. In the above figure, A, B, C and D are data points.
6. Line segments: Every two data points are joined together by a straight line. In the above figure, AB, BC and CD are line segments.

## Make a Line Graph

Steps to be followed while graphing a line graph are as follows:
1. Identify independent and dependent variables from the data. This can be done by simply looking at the data and type of variables.
2. Choose a scale for independent data and mark it at X-axis.
3. Put the label (name of independent variable) for X-axis.
4. Choose a scale for dependent data and mark it at Y-axis.
5. Put the label (name of dependent variable) for Y-axis.
6. Plot the points on the graph.
7. Join the points with straight lines.
Let us consider an example.

### Solved Example

Question: Draw a line graph for the following data:
 Months January February March April May June Average Temperature 12$^o$C 18$^o$C 25$^o$C 35$^o$C 40$^o$C 42$^o$C

Solution:
1. Independent variable is "Months" and dependent variable is "Average temperature".
2. We chose a scale on X axis: 1 point = 1 month.
3. We labeled "Months" on X axis.
4. We chose a scale on Y axis: 1 point = 10$^o$C.
5. We labeled "Average Temperature" on Y axis.
6. We plotted the 12, 18, 25, 35, 40 and 42.
7. We have joined them with straight lines.
In this way, we obtained the following graph:

## Types of Line Graphs

Line graphs are widely used to estimate rate of change of a quantity as well as to compare two or more different variables. In this way, we have following 3 types of line graphs:
1. Single line graph
2. Double line graph
3. Multiple line graph
Single Line Graph: This is a graph which contains information about one data set. It shows peaks and valleys or ups and downs of a single set of data. It has one line in its graph. This is a kind of graph which we have been discussing above.
Double Line Graph: This is a graph which contains information about two data sets. It is useful in making comparisons between two sets of data. It has two lines in its graph.
Multiple Line Graph: This is a graph which contains information about more than two data sets. It is useful in making comparisons between multiple sets of data. It has multiple lines in its graph.

## Straight Line Graph

Straight line graph is a graph in which independent and dependent variables are so connected that they represent a straight line. If dependent variable is directly proportional to independent variable, then eventually the graph would appear as a straight line. All of the three types discussed above can be straight line graphs. In the following figure, a graph is sketched between time and distance traveled. Distance covered is directly proportional to time (provided that speed is constant), therefore its graph has come out to be a straight line .

## Double Line Graph

A double line graph has two lines in a graph. It takes one independent variable to be marked on X-axis, while two dependent variables on Y-axis. It is useful to make instant conclusions about comparison of two sets of data. The results can be interpreted by just looking at it. Make both the lines in different colors (if possible) or use different data point symbols to make it easily differentiable.

## Double Line Graph Example

Let us consider few examples of double line graphs

### Solved Examples

Question 1: A record monthly saving of Jack and Barbara (in USD) are listed in the following table. Sketch a double line graph.

 Jan Feb Mar April May Jack 1000 2000 2500 3000 2000 Barbara 1500 1000 2000 1000 1500

Solution:
The double line graph of the above data is given below:

Question 2: The profit of two companies at the year end is tabulated below. Draw a double line graph and compare the two outcomes.
 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 Company A 3 5 6 7 4 6 Company B 1 3 4 5 4 2
The profit is calculated in million dollars.
Solution:
The double line graph of above data is given below:

By comparing both the lines, we can easily say that overall profit of company A is greater than that of company B and profits of both the companies were equal in year 2004-05.

## Interpreting Line Graphs

Line graph gives a lot of information about the data. Line graph can be used for interpreting various results and outcomes based on which different strategies can be generated. However, interpretation of a line graph depends upon the presentation of the data. Few interpretations are listed below:
• Determination of dependent and independent variable.
• Determination of item measured and its unit.
• Determination of rate of change of an item.
• Comparison of two or more data sets in case of double line and multiple line graphs.
• Estimating peaks or ups and valleys or downs.
• Forecasting future results.

## Line Graph Examples

Few examples based on line graphs are given below:

### Solved Examples

Question 1: Construct a line graph for the information given below and answer the following questions by the graph:
 Months January February March April May June Number of cars sold 20 35 25 40 45 30
• Which month were the highest number of cars sold?
• Which month were the lowest number of cars sold?
• What is the range of cars sold from January to June?
• How many months had sell less than 30?

Solution:
The line graph of the given data is as follows:

• The highest number of cars were sold in the month of May and is 45.
• The lowest number of cars were sold in the month of January and is 20.
• The range of cars sold from January to June = 45 - 20 = 25
• January and March months had sell less than 30.

Question 2: Temperatures of New York and San Diago were recorded on 7 consecutive days. Construct a double line graph and answer the following questions:
 Monday Tuesday Wednesday Thursday Friday Saturday Sunday New York 14 15 13 16 14 16 15 San Diago 16 15 17 18 16 15 17
• Which days were the maximum and minimum temperature noted in New York?
• Which day were the maximum and minimum temperature noted in San Diago?
• On which day, exactly same temperature was noted in both the cities?

Solution:
The double line graph of the given data is:

• Maximum temperature was noted in New York on Thursday and Saturday and was 16$^o$C. Minimum temperature was noted in New York on Wednesday and was 13$^o$C.
• Maximum temperature was noted in San Diago on Thursday and was 18$^o$C. Minimum temperature was noted in San Diago on Tuesday and Saturday and was 15$^o$C.
• On Tuesday, exactly same temperature (15$^o$C) was noted in both the cities.

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