**Introduction**

Statistics is a branch of mathematics that deals with collecting, organising, presenting, analysing and interpreting data It is very important to know the objective of collecting the data. After the data has been collected it has to be presented in such a form that helps one to study easily and draw inferences quickly. This is called the distribution of presentation or organisation of data. Statistical data can be presented in the form of tables, pictures, graphs and diagrams with have a lasting effect on the observer’s mind. One such tool for presenting the statistical data is line graphs. Let us learn more about line graphs.

**Definition**

**A line graph is a type of chart or graph that is used to show information that changes over time.** In other words, a line graph is a chart that helps us to visualise the value of something over time. A line graph has two axis – a horizontal axis which is known as the x – axis and a vertical axis which is known as the y – axis. The x-axis is also called the independent axis because its values do not depend on anything.

Before we move ahead with an understanding of the steps involved in the construction of line graphs, let us learn what we mean by dependent and independent variables.

**Dependent and Independent Variables**

While constructing graphs we generally have values of one value corresponding to different values of other variables. The variable which takes values freely, that is, whose values do not depend on the values of other variable, is called an independent variable and the variable whose values depend on the values taken by the other variable is known as the dependent variable. Let us take an example. The runs scored by a cricket team in a match depend upon the number of overs bowled by the other team. Therefore, in this case, the number of overs is an independent variable and the runs scored is a dependent variable. Similarly, the perimeter of a square depends upon the length of a side of the square. Therefore, the perimeter of a square is a dependent variable while the length of a side of the square is an independent variable.

Now let us learn about the parts of a line graph.

**Parts of a Line Graph**

The following are the parts of a line graph –

**Title** – The title of the graph tells us what the graph is all about. In other words, the title of a graph tells us what information is represented on the graph. This helps us identify what we are about to look at in the graph.

**Labels** – Also, known as legends, the labels tell us what each line represents. The horizontal axis across the bottom and the vertical label along the side tell us what kinds of data are being shown on the line graph.

**X – axis – **In line graphs, the x-axis runs horizontally ( flat ). Typically, the x – axis has numbers representing different time periods or names of things being compared.

**Y – axis** – In line graphs, the y-axis runs vertically up and down. Typically, the y-axis has numbers for the amount of stuff being measured. The y-axis usually starts counting at 0 and can be divided into as many equal parts as we want to.

**Scales** – How much and how many is the information provided by the scales on the graph which are represented by the horizontal scale across the bottom and the vertical scale along the column.

**Points** – The points or dots on the graph represent the ( x , y ) coordinates or ordered pairs. More than one data line can be present in a line graph. Here, data on the horizontal axis ( x- axis ) is the independent variable, and data on the vertical axis ( y – axis ) is the dependent variable. The points represent the most important part of the line graph, i.e. the information. Line graphs can present more than one group of data at a time.

**Lines** – Straight lines connecting the points give the projected values between the points.

**Plotting points on a Line Graph**

Consider the following example.

The table shows the daily earnings of a store for five days.

Day: | Mon | Tue | Wed | Thurs | Fri |

Earnings: | 300 | 450 | 200 | 400 | 650 |

Let us plot the points above on a graph.

In order to plot the graph, the following steps will be followed –

- Identify independent and dependent variables from the given information
- Label the independent variable along the x – axis and the dependent variable on the y – axis.
- Choose an appropriate scale for plotting points. We may choose different scales along the x-axis and the y – axis.
- Plot each ordered pair and join the plotted points to get the desired graph.

The following will be the line graph of the given data –

**Reading a Line graph**

Let us now learn how to read a line graph.

The following steps should be followed to read a line graph –

- The first step is to read both the axis and understand what is represented by them.
- In the next step, the values of the points situated in the lines of the graph are examined.
- The rise and the fall of the lines are carefully observed so as to understand the trend of changes in the data.

Let us understand it through an example.

Consider the following line graph showing the total number of animals in a zoo.

We can see that the graph shows the total number of animals over certain years. Can we find the information about in which year did the zoo have the largest number of animals? Yes, we can, by carefully observing the data plotted on the graph. If we look at the points on the graph, we can see that the highest point for the number of animals is for the year 2002 which is 600. Hence from the graph, we can conclude that there were 600 animals in the zoo in 2002 which is the maximum of the given data.

**Types of Line Graphs**

There are five types of lines graphs, mainly –

- Simple Line Graph
- Multiple Line Graph
- Compound Line Graph
- Vertical Line Graph
- Horizontal Line Graph

Let us learn about them one by one.

**Simple Line Graphs**

Simple line graphs are graphs where only one line is plotted on the graph. Such graphs show the relationship between two variables only. For instance, below is an example of a simple graph –

**Multiple Line Graphs**

Multiple line graphs are line graphs where more than one line is plotted on the graph on the same set of axis. Such graphs represent the change over a period of time for two or more variables and are helpful in comparing similar items over the same period of time. For instance, below is an example of a multiple graph –

**Compound Line Graphs**

Compound graphs are the graphs that are formed if the information can be subdivided into various types. In a compound graph, the topmost line displays the total and the line below tells the part of the total. For instance, below is an example of a compound graph –

**Vertical Line Graph**

Vertical line graphs are graphs where a vertical line continues from each data point to the horizontal axis. In such graphs, the data line is parallel to the y – axis. For instance, below is an example of a vertical line graph –

**Horizontal Line Graph**

Vertical line graphs are graphs where a horizontal line continues from each data point to the vertical axis. In such graphs, the data line is parallel to the x – axis. For instance, below is an example of a horizontal line graph –

**Advantages of a Line Graph**

There are a number of advantages of a line graph. Some of these advantages are –

- A line graph is useful in showing the changes and trends over a time period.
- Small changes that are otherwise to show in other graphs can be easily represented using line graphs.
- Line graphs are simple, efficient and easy to understand.
- When a comparison is required, more than one line graphs can be plotted on the same graph.

There are some disadvantages of line graphs as well. Let us learn about them.

**Disadvantages of a Line Graph**

There are a number of disadvantages of a line graph. Some of these disadvantages are –

- Too many lines on a line graph can be confusing and difficult to interpret.
- A line graph is not suitable when there is wide range of data that needs to be plotted.
- A line graph is only useful for plotting of numerical values and data and not suited for fractional and decimal values.

**Line Graph vs Scatter Plot**

How is a line graph different from a scatter plot? The difference lies in their definitions themselves. A line graph is a type of chart or graph that is used to show information that changes over time. On the other hand, a scatter plot is a means to represent data in a graphical format. A simple scatter plot makes use of the Coordinate axes to plot the points, based on their values. The difference between a line graph and a scatter plot can be summarised as under –

Line Graph | Scatter Plot |

A line graph is a type of chart or graph that is used to show information that changes over time. | A scatter plot puts a point representing a single realization of a tuple of data. |

For example, if you measure the change in temperature of a city over different time of the day. | For example, if you measured people’s height and weight, you could create a scatter plot where one axis represented height and one represented weight. |

It is used to show continuous data over a period. | It is used to plot two groups of numbers as one series of x and y coordinates. |

Data is evenly distributed in a line graph | Data is not evenly distributed in a line graph |

Lien segments are used to join the points on a line graph | The points on the graph are not joined with each other. |

Line graphs are not suitable for representing large amounts of data | Scatter plots can be used to represent large amounts of data. |

**Line Graphs vs Histogram**

We know that a histogram is a type of bar chart that is used to represent statistical information by way of bars to display the frequency distribution of continuous data. It indicates the number of observations that lie in-between the range of values, which is known as class or bin.

The following are the key differences between a line graph and a histogram

Line Graph | Histogram |

A line graph is a type of chart or graph that is used to show information that changes over time. | The Histogram refers to a graphical representation that shows data by way of bars to display the frequency of numerical data |

For example, if you measure the change in temperature of a city over different time of a day. | A histogram is used to represent the Distribution of non-discrete variables. |

It is used to show continuous data over a period. | Histogram used for distribution of non-discrete variables |

Data is evenly distributed in a line graph | Data is not evenly distributed in a histogram |

Lien segments are used to join the points on a line graph | Bars are used to join the points in a histogram |

Line graphs are not suitable for representing large amounts of data |

**Solved Examples**

**Example 1** The quantity of petrol filled in a car and the cost of petrol are given in the following table –

Litres of Petrol filled : | 10 | 15 | 20 | 25 |

Cost of Petrol : | 500 | 750 | 1000 | 1250 |

Draw a line graph representing the above data. Also, find the cost of 12 litres of petrol using the line graph.

** Solution** Let us take petrol filled on the x – axis and the cost of petrol on the y – axis.

Let us now choose the following scale –

On x – axis = 2 litres and on y – axis 1 cm = £ 100

Now, using this scale, let us plot the given ordered pairs on the line graph. We will get,

We can see above that by joining the points on the graph we have obtained the line graph for the given data.

Now, to find the cost of petrol using the graph, we will proceed as follows –

We will find 12 on the horizontal axis that represents the quantity of petrol in litres.

We can see from the graph that the corresponding point on the y axis is 600. Hence, the cost of 12 litres of petrol would be £ 600.

**Example 2** The table shows the daily sales in RM of different categories of items for five days.

Day | Mon | Tues | Wed | Thurs | Fri |

Drinks | 300 | 450 | 150 | 400 | 650 |

Food | 400 | 500 | 350 | 300 | 500 |

Construct a line graph for the frequency table.

**Solution** We have been given the following data and are required to construct a line graph for the same –

Day | Mon | Tues | Wed | Thurs | Fri |

Drinks | 300 | 450 | 150 | 400 | 650 |

Food | 400 | 500 | 350 | 300 | 500 |

The line graph for the above data would be –

**Key Facts and Summary**

- A line graph is a type of chart or graph that is used to show information that changes over time.
- The variable which takes values freely, that is, whose values do not depend on the values of other variable, is called an independent variable and the variable whose values depend on the values taken by the other variable is known as the dependent variable.
- The title of the graph tells us what the graph is all about. In other words, the title of a graph tells us what information is represented on the graph.
- The horizontal axis across the bottom and the vertical label along the side tell us what kinds of data are being shown on the line graph.
- How much and how many is the information provided by the scales on the graph which are represented by the horizontal scale across the bottom and the vertical scale along the column.
- The points or dots on the graph represent the ( x , y ) coordinates or ordered pairs.
- Straight lines connecting the points give the projected values between the points.
- In line graphs, the y-axis runs vertically up and down. Typically, the y-axis has numbers for the amount of stuff being measured.
- In line graphs, the x-axis runs horizontally ( flat ). Typically, the x – axis has numbers representing different time periods or names of things being compared.
- Simple line graphs are the graphs where only one line is plotted on the graph.
- Multiple line graphs are line graphs where more than one line is plotted on the graph on the same set of axis.
- Compound graphs are the graphs that are formed if the information can be subdivided into various types.

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