Interpretation of Graphs
You survey 15 students in your class about their favorite colour. Everyone named different colors, some chose the same color and you noted their responses. Now, it is very difficult to state everyone’s opinion every time. Therefore, we can use different types of methods to represent the information. We can use pictorial representations, different types of graphs or line plots, and so on to represent the data. Using this type of representation, we can easily study this information.
Picture Graph
A picture graph shows data using pictures or symbols. The key to a picture graph is the value of each picture. Every picture gives a predefined number that we assume. The value of one picture, or symbol, can be equal to or greater than 1.
Steps to make a picture graph:
Step 1: Write the title at the top of the picture graph.
Step 2: Label a row for each category.
Step 3: Look at the number in the frequency table. Choose a value for the key of every picture.
Step 4: Use the key to decide how many symbols we need for each category.
Step 5: Draw the calculated symbols in respective rows for each category.
Suppose you survey 20 students about their favorite type of party and note the result. But marking 20 students every time and finding their answers is a very tedious task. So we can use another method to represent the data
In this representation, we can very easily show all four types of the party the children like. Among the 20 students, 4 selected the bounce house, 8 selected skating, 6 selected pools, and 2 selected costume parties. This symbolic representation is called a pictorial representation.
In this, we have used the picture ‘ 
’ for each student. If the given data is large, then use each face ‘ ’ to represent two students.
Then we can show the same information through a pictorial graph as,
In this, we represented the same data using even fewer faces or pictures. If the survey is for large data, we can set the key accordingly. In the picture graph, we can also use the half key to represent the data.
For example, in the above picture graph, we can use the half-face ‘ 
’ to represent one student. Similarly, for any type of information or data, we can have different pictures and make our survey user-friendly and easy to understand.
Frequency Table
A frequency table refers to the number of times an event or a value occurs.
If we survey some data and then make a table by listing the items, the table is called a frequency table. Here is an example of a frequency table:
Bar Graph
A bar graph is also a very common and useful method to represent data. In the picture graph, we used symbols. Similarly, in the bar graph, bars are used to show information.
So, a bar graph is the representation of data in the form of rectangular bars.
Steps to make a bar graph:
Step 1: Write the title at the top of the bar graph.
Step 2: Label a row for each category.
Step 3: Look at the number in the frequency table. Use a scale such that most of the bars end on a grid line.
Step 4: Label the scale.
Step 5: Draw and shade a bar for each category. The bar graph will be obtained.
For example,
Four friends, David, John, Robert, and Thomas went to the market. They want to buy some chocolates. Each friend has a different amount of money.
Name of friend | Money ($) |
|---|---|
David | 12 |
John | 8 |
Robert | 6 |
Thomas | 2 |
We can show that in the bar graph as,
In a bar graph, when a bar ends halfway between two grid lines, the data value for the bar is halfway between two numbers on the scale.
Line Plot
A line plot uses marks above a number line to show data values.
The frequency of different types of data is mentioned above a number line, often through a cross or a circle symbol.
Steps to make a line plot:
Step 1: First, write the title at the top of the line plot.
Step 2: Observe the numbers in the frequency table or data provided. Think of a scale that shows all of the data values.
Step 3: Draw a number line using the scale and label it.
Step 4: Mark an ‘X’ for each data value.
For example, you survey the number of family members in different families. The frequency of families is noted as,
The number of family members in each family:
6 | 5 | 8 |
5 | 8 | 9 |
4 | 6 | 8 |
6 | 5 | 8 |
Now, make a number line and label the line. Put the ‘X‘ mark above the respective labels.
Then the line plot is obtained as:
Solved Interpreting Graphs Examples
Example 1:
Use the graph to answer the question.
How many national forests are in-country 1?
How many national forests are in-country 2?
Solution:
Each ‘ 
’ = 4 forests.
There are 4 ‘ ’s in the row for country 1.
So, Number of forests in country 1 = 4 × 4 =16
There are 16 national forests in country 1.
Again, there are 2 ‘ ’s and one half tree symbol ‘
’ in the row for country 2.
2 ‘ ’s = 2 × 4 = 8
’ = 4 ÷ 2 = 2
There are 8 + 2 = 10 national forests in country 2.
Example 2: The bar chart below shows the favorite subjects of students in a class. Make a frequency table from the given data.
Solution:
First, observe the height of each bar. Make a table with two columns. Write each subject in the first column. Then write down the frequency of each subject.
The frequency table for the given data is,
Subject | Frequency |
|---|---|
English | 52 |
Physics | 41 |
Mathematics | 39 |
Chemistry | 36 |
Other | 25 |
Example 3: Use the graph to answer the questions.
How many students like cats?
Which animal is the most favorite?
Solution:
The bar for the cat ends at number 10. So, there are 10 students who liked cats.
The length of the bar for the elephant is the longest. So, elephants are the most favorite animal among students.
Example 4: Make a bar graph using the information provided.
Solution:
From the frequency table, we can draw a bar graph
The names of the different planets are marked horizontally and the scale is marked vertically. We can see that the earth is the most favorite planet.
Example 5:
Make a picture graph of the same as in the previous example. Which representation is easier to understand?
Solution:
Since all the numbers are divisible by 5, we choose the key as 5 students for each ‘ 
’ Then make a picture graph as shown.
The heading of the picture graph is “Favorite Planet” and in each row, the number of favorite planets is represented.
Now to calculate the exact number from the bar picture graph is calculative. The data in the bar graph shows the exact number of different frequencies. Therefore, the bar graph is easier.
Example 6: Different students went to play a game. Each student brings a number of toys as shown below:
Number of toys:
5 | 6 | 5 |
7 | 4 | 5 |
6 | 7 | 7 |
6 | 5 | 5 |
Make a line plot using the data provided.
Solution:
The number of toys for each student is provided.
A minimum of 4 and a maximum of 7 toys are there for the students. So, make a number line of 4 and 7.
Count the frequency of every number. Then, mark the respective number of crosses on the numbers.
We can represent data through pictorial graphs, bar graphs, line plots, histograms, and so on.
The representation of data in different ways makes the data easily accessible. We can therefore understand and analyze different types of data quickly.