Drawing Graphs: We have seen graphs in newspapers, on television, in magazines, in books, and elsewhere. The term graph refers to an organised pictorial representation of data. We have all heard the phrase that a picture can tell a thousand stories. On the other hand, a graph may express a thousand words and convey a variety of stories. On a graph, each point, stroke colour, and shape have a different meaning that aids in reading the diagram.

This article will look at what a graph is, what components are needed to draw graphs, different types of graphs, draw graphs, and some solved examples.

What is a Graph?

A graph is a pictorial representation or diagram that organises data or values into a logical order.

The points on the graph often show the link between two or more items.

Components of a Graph

1. A title: The title offers a short explanation of what is in the graph. This helps the reader know what they are about to look at. The above chart shows the rainfall from April to July.

2. \(Y\)- axis: It is a vertical scale with marks and labels. The \(Y\)-axis runs vertically (up and down). Typically, the \(Y\)-axis has numbers for the parameter being measured. The \(Y\)-axis usually starts counting at \(0\) and can be divided into as many equal parts as you want to. In the above line graph, the \(Y\)-axis is measuring the amount of rainfall.

3. \(X\)- axis: The \(X\)-axis runs horizontally (flat). Typically, the \(X\)-axis has numbers representing different time periods or names of things being compared. In the above line graph, the \(X\)-axis indicates the names of the months.

4. Data categories or Axis labels: Each axis needs a descriptive category indicating which variable is represented. For example, the \(Y\)-axis categories might read “Color”, and the \(X\)-axis categories might read “Number of students.”

5. Data values: Plot values are the values displayed on the chart for each data plot (line, column, bar, or pie).

6. Scale: In graphs, a scale is a set of fixed interval marks that define the relationship between the units used and their representation on the graph.

Learn All Concepts on Line Graph

Types of Graphs

Different types of graphs are discussed below:

1. Line Chart

This is the most basic form of a graph. It presents information as a series of data collected throughout time. Markers are the names given to these data points. Line graphs help display how something changes over time.

How to Draw a Line Graph?

1. Draw two lines perpendicular to each other intersecting at \(O\) on a graph. The \(X\)-axis is horizontal, while the \(Y\)-axis is vertical. Mark points along the \(X\)-axis at equal intervals and write the names of the data items whose values will be marked.
2. Choose an appropriate scale for the \(Y\)-axis based on the provided data.
3. Now it’s time to mark the points.
4. Using a ruler, connect each point to the one before it. As a result, a line graph is created.

2. Bar Graph

A bar chart is a visual representation of data in uniformly spaced vertical or horizontal bars. They can be drawn on the horizontal axis (say, the \(X\)-axis) with equal spacing between them to represent the variable. The variable’s values are shown on the vertical axis (say, the \(Y\)-axis), and the heights of the bars are determined by the variable’s values.

How to Draw a Bar Chart?

1. Determine the appropriate scale for the graph based on the size of the paper on which it will be created.
2. Draw two lines perpendicular to each other. Then label the horizontal and vertical lines as \(X\)-axis and \(Y\)-axis, respectively.
3. To represent the values in the data, draw rectangular bars of equal width.

The bar chart given below shows the sale of trousers in a shop from Monday to Saturday.

3. Pie Chart

A pie chart is a form of a graph that uses a circular diagram to represent data. The graph’s components are proportionate to the percentage of the total in each group. In other words, the size of each slice of the pie is proportional to the size of the group. The complete “pie” represents \(100\% \) of a whole, whereas the “slices” represent parts of the total.

How to Draw a Pie Chart?

1. Sort the data into the relevant categories.
2. Add all the given values to get the total value of the data.
3.Divide the value of each category by the total value.
\(\frac{{{\text{Value}}\,{\text{of}}\,{\text{each}}\,{\text{category}}}}{{{\text{Total}}\,{\text{value}}}}\)
4. Make a percentage out of the result by multiplying it by \(100.\)
5. To convert the data into degrees by multiplying it with \({360^ \circ }.\)

4. Histogram

Histograms are a type of bar graph that displays data distribution.

Although a histogram and a bar graph appear to be quite similar, they differ according to the data level. The other difference is that there are gaps between the bars in a bar graph, but there are no gaps between the bars in a histogram.

How to Draw a Histogram?

1. On the vertical axis, write frequencies.
2. On the horizontal axis, write the lower value of each interval. Label this axis with the type of data shown (the price of birthday cards, etc.)
3. Draw a bar extending from the lower value of each interval to the lower value of the next interval. The height of each bar should be equal to the frequency of its corresponding interval.

5. Exponential Graph

Exponential graphs represent the exponential functions that use the table of the values and plotting the points on graph paper. The exponential functions are the inverse of the logarithmic functions.

It can be an increasing or decreasing type of curve based on the function.

How to Draw Exponential Graphs?

1. Make a table with the points.
2. At least three points from the table, including the \(y\)-intercept, should be plotted.
3. Make a smooth curve connecting the points.

6. Logarithmic Graph

Logarithmic functions are the inverse of the exponential functions. However, the method to draw the graph is similar. Make a table of the values to draw the logarithmic graphs and then mark the points correspondingly on graph paper.

The graph of any \(\log \) function will be the opposite of an exponential function. The diagram is shown below for ease of understanding.

Importance of a Graph

Graphs are a popular way to represent data relationships visually. A graph aims to display too much complex data to be effectively expressed in text and limited space. However, graphs should not be used for small quantities of data that can be represented in a single sentence.

Uses of Graph

Graphs and charts are essential since they are used to communicate information visually. These are used in various fields, including newspapers, businesses, and magazines, to display economic data, annual reports, and profits and losses. They are also used in math and other branches of science, such as chemistry and physics, to demonstrate the variations and relationships between two variables.

Solved Examples on Drawing Graphs

Q.1. Given below is a line graph showing the height changes in Elizabeth as she grows. Observe the graph and answer the question below.

What was Elizabeth’s height at 8 years?
Ans: The height of Elizabeth at \(8\) years is \(65\) inches.

Q.2. Draw a histogram for the following 100 people whose daily wages are given below:

Daily wages	\(0 – 50\)	\(50 – 100\)	\(100 – 200\)	\(200 – 250\)	\(250 – 450\)	\(450 – 500\)
Numberof people	\(5\)	\(10\)	\(16\)	\(7\)	\(48\)	\(14\)

Ans: The histogram using the above chart is drawn as shown below:

Q.3.

The population of a town was recorded every twenty years from 1900 to 2000. The results are shown in the line graph. By how much did the population increase between 1920 and 1980?
Ans: On the vertical axis, every \(5\) squares represent a population of \(1000.\)
So each one square represents \(200.\)
The dot for the year \(1920\) is \(1\) square above \(1000.\)
Therefore the population in \(1920\) was \(1200.\)
The population in \(1980\) was \(4000.\)
Therefore between \(1920\) and \(1980\) the population increased by \( = 4000 – 1200 = 2800\)

Q.4. Draw the graph of \(f\left(x \right) = 3x.\)
Ans: Make a table of values.

Plots the points

Connect the points using a smooth curve.

Q.5.

The bar graph showed the results when a die was thrown several times. How many sixes were thrown?
Ans: The number of sixes is given by its frequency, or how high the bar is for the score \(6.\)
So, look for \(6\) across the horizontal axis and then read off its frequency on the vertical axis.
There were \(3\) sixes.

Learn Concepts on Bar Graphs

Summary

In this article, we looked at what a graph is and what components are needed to draw graphs. We saw different types of graphs, such as line graph, bar graph, pie chart, histograms, exponential graph, logarithmic graph etc., and how to draw graphs, the importance of graphs, as well as uses of the graph along with some solved examples.

FAQs on Drawing Graphs

Q.1. What are the 5 parts of a graph?
Ans: The \(5\) parts of the graph are title, \(X\)-axis, \(Y\)-axis, data values and data categories.

Q.2. What are the types of graphs?
Ans: The types of graphs are:
1. Line graph
2. Bar graph
3. Pie chart
4. Histogram
5. Exponential graph
6. Logarithmic graph

Q.3. How do you draw a simple graph?
Ans: Step 1: Determine the variables.
Step 2: Establish the variable’s range.
Step 3: Determine the graph’s scale.
Step 4: Title the graph, number and label each axis.
Step 5: Choose your data points and put them on the graph.
Step 6: Make a graph.

Q.4. What can be learned from graphs?
Ans: We can convert the large data into visual form with the help of graphs and understand the information quickly and easily.

Q.5. What are graphs used for in everyday life?
Ans: Graphs are used in various fields, including newspapers, businesses, and magazines, to display economic data, annual reports, and profits and losses.