Drawing a Bar Graph

In a previous example, Shri Nilesh prepared a frequency table representing the sweet preferences of the students in his class. Let’s try to prepare a bar graph to present his data —

1. First, we draw a horizontal line and a vertical line. On the horizontal line, we will write the name of each of the , equally spaced, from which the bars will rise in accordance with their frequencies; and on the vertical line we will write the frequencies representing the number of .

2. We must choose a scale. That means we must decide how many students will be represented by a unit length of a bar so that it fits nicely on our paper. Here, we will take unit length to represent 1 student.

3. For jalebi, we therefore need to draw a bar having a height of units (which is the frequency of the sweet jalebi), and similarly for the other sweets we have to draw bars as high as their frequencies.

4. We, therefore, get a bar graph as shown below —

When the frequencies are larger and we cannot use the scale of 1 unit length = 1 number (frequency), we need to choose a different scale like we did in the case of .

The number of runs scored by Smriti in each of the 8 matches are given in the table below.

In this example, the minimum score is 0 and the maximum score is 100. Using a scale of 1 unit length = l run would mean that we have to go all the way from 0 to 100 runs in steps of l. This would be unnecessarily tedious. Instead, let us use a scale where 1 unit length = 10 runs. We mark this scale on the vertical line and draw the bars according to the scores in each match. We get the following bar graph representing the above data.

The following table shows the monthly expenditure of Imran’s family on various items.

To represent this data in the form of a bar graph, here are the steps —

• Draw two perpendicular lines, one horizontal and one vertical.

• Along the horizontal line, mark the ‘items’ with equal spacing between them and mark the corresponding expenditures along the vertical line.

Take bars of the same width, keeping a uniform gap between them. • Choose a suitable scale along the vertical line. Let, 1 unit length = Rs 200, and then mark and write the corresponding values (Rs 200, Rs 400, etc.) representing each unit length.

Finally, calculate the heights of the bars for various items as shown below —

Here is the bar graph that we obtain based on the above steps:

Use the bar graph to answer the following questions:

1. On which item does Imran’s family spend the most and the second most?

It is clear from the graph that Imran’s family spend the most on and second most on .

2. Is the cost of electricity about one-half the cost of education? YesNo.

It is clear from the bar graph that the cost of electricity about one-half the cost of education because we see in graph the cost of electricity is ₹ 400 and the cost of education is ₹ 800 i.e. amount ₹ 400 is the one-half off .

3. Is the cost of education less than one-fourth the cost of food? YesNo.

In the graph, we see that the cost of education is ? 800 and the cost of food is ₹ .

Hence, one-fourth of the cost of food = 34004 = ₹ 850 ∴ ₹ 800 < ₹ 850

Hence, the cost of education is lessgreater than one-fourth the cost of food.

Figure it out 6

1. Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected.

Mites	Caterpillars	Beetles	Butterflies	Grasshoppers
6	10	5	3	2

Help her prepare a bar graph representing this data.

2. Pooja collected data on the number of tickets sold at the Bhopalrailway station for a few different cities of Madhya Pradesh over a two-hour period.

She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph.

d. Draw the correct bar for Sagar.

3. Chinu listed the various means of transport that passed acrossthe road in front of his house from 9 a.m. to 10 a.m.

a. Prepare a frequency distribution table for the data.

Frequency distribution table for the given data is given below.

4. Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared.

Let the outcomes of 30 times roll of a die be

Number on the die	Tally Marks	No of Throws
1
2
3
4
5
6

a. The minimum number of times : and .

b. The maximum number of times :

c. Find numbers that appeared an equal number of times : and .

5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches.

6. The following pictograph shows the number of tractors in five different villages.

Observe the pictograph and answer the following questions.

7. The number of girl students in each class of a school is depicted by the pictograph.

Observe this pictograph and answer the following questions:

8. Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka’s Bagalkote and Vijaypura districts. The government took an initiative to protect this breed by providing support to those who adopted these dogs. Due to this initiative, the number of these dogs increased. The number of Mudhol dogs in six villages of Karnataka are as follows — Village A : 18, Village B : 36, Village C : 12, Village D : 48, Village E : 18, Village F : 24

Prepare a pictograph and answer the following questions:

9. A survey of 120 school students was conducted to find out which activity they preferred to do in their free time.

Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?

10. Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. Details of the saplings they planted are as follows.

a. The total number of saplings planted on Wednesday and Thursday is: + = saplings.

b. The total number of saplings planted during the whole week is: + + + + + = saplings.

c. The greatest number of saplings were planted on and the least number of saplings were planted on .

Why do you think that is the case? Why were more saplings planted on certain days of the week and less on others? Can you think of possible explanations or reasons? How could you try and figure out whether your explanations are correct?

11. The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in four-year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?

Solution :

There are a few mistakes in the graph.

1. No. of tigers in 2006 was but shown less in the graph.

2. No. of tigers in 2014 was but shown more in the graph.

3. No. of tigers in 2018 was but shown less in the graph.

• Like pictographs, bar graphs give a nice visual way to represent data. They represent data through equally-spaced bars, each of equal width, where the lengths or heights give frequencies of the differentsame categories.

• Each category is represented by a bar where the length or height depicts the corresponding (for example, cost) or quantity (for example, runs).

• The bars have uniform spaces between them to indicate that they are free standing and represent equalun equal categories.

• The bars help in interpreting data much faster than a frequency table. By reading a bar graph, we can compare frequencies of differentsame categories at a glance.

• We must decide the scale (for example, 1 unit length = 1 student or 1 unit length = Rs 200) for a bar graph on the basis of the data including the minimum and maximum frequencies, so that the resulting bar graph fits nicely and looks visually appealing on the paper or poster we are preparing. The markings of the unit lengths as per the scale must start from zero.