Bar Graph

We learn how to represent the data on the bar graph.

Bar graphs are one of the many methods used to present data in a visual form. Bar graphs usually present data grouped in intervals, which depicts the frequencies of values in a particular interval. 

Data can be represented by bars (like rectangle) whose lengths represent numerical values. One can use horizontal or vertical bars. Instead of rectangles one way even use line segments in such graphs.

Scale

To represent different numbers, first we need to decide what number a unit length of the bar represents. For example, if the data is of the population of villages, we can choose 1 cm of the bar to represent 500 people. This relation between the unit length of the bar and the quantity it represents is called the scale of the bar graph. The chosen scale is sometimes mentioned in the bar graph. In this case, the scale would be written as 1 cm : 500 people.

One can choose any scale for a graph. Obviously, the scale should be such that all the base of the graph fit on the paper on which it is drawn.

Interval is the space between each value on the scale of a bar graph. They are chosen based on the range of the values in the data set.

Solved Examples on Bar Graph:

1. Observe the bar graph given below and answer the questions that follow.

Answer the following questions.

(i) How many students have read less than 11 books?

(ii) How many students have read 15 - 20 books?

(iii) How many students have read 25 - 30 books?

(iv) How many students have read more than 15 books?

Solution:

The above graph is showing a relationship between number of students are the books read. Here we find that the interval chosen on the x-axis are 1 - 5, 6 - 10, 11 - 15, 15 - 20 and 25 - 30.

(i) The two bars on the x-axis(1 - 5, 6 - 10) show the number of students who have read books less than 11. The numbers on the y-axis show: 10 + 8 = 18.

(ii) The number on the y-axis corresponding to the bar 15 - 20 shows 11 students.

(iii) The number on the y-axis corresponding to the bar 25 - 30 shows 3 students.

(iv) The two bars on the y-axis show the number of students who have read books more than 15 books. The numbers on the y-axis show: 11 + 3 = 14.

Questions and Answers on Bar Graph:

1. Choose the right answer.

(i) If one block in a bar graph represents 5 students, how many blocks will represent 20 students?

(a) 2               (b) 3               (c) 4               (d) 5

(ii) The representation of data in the form of pictures is a:

(a) Data Handling       (b) Tally Mark      (c) Bar Graph      (d) Pictograph

(iii) All bars in a bar graph have equal:

(a) Size               (b) Width              (c) Length               (d) Axis

Answers:

1. (i) (c) 4 

(ii) (d) Pictograph

(iii) (b) Width

2. Choose the right answer and fill in the blank.

(i) __________ can be represented by both words and numbers.

(a) Data        (b) Tally Mark      (c) Data Handling       (d) Pictograph

Answer:

2. (a) Data 

3. Look at the bar graph given below and answer the questions.

(i) Which sport is liked by maximum students?

(a) Cricket

(b) Badminton

(c) Chess

(d) Football

Answer: (b) Badminton

(ii) Which sport is liked by minimum students?

(a) Cricket

(b) Badminton

(c) Chess

(d) Football

Answer: (c) Chess

(iii) Which sport is liked by equal number of students?

(a) Cricket and Chess

(b) Cricket and Football

(c) Badminton and Football

(d) None of these

Answer: (b) Cricket and Football

(iv) How many students like Chess?

(a) 3

(b) 4

(c) 6

(d) 10

Answer: (d) 10

(v) How many students like Cricket?

(a) 10

(b) 15

(c) 20

(d) 25

Answer: (b) 15

(vi) Which sport is liked by 10 students?

(a) Cricket

(b) Badminton

(c) Chess

(d) Football

Answer: (c) Chess

5. A survey of 36 students of a class was done to find out the mode of transport used by them while commuting to their school. the collected data is shown in the table given below. Represent the data in the form of a bar graph.

Now answer the given questions:

(i) Give a suitable title for the graph.

(ii) How many students come by car?

(iii) Which mode of transport is used by most of the students?

(iv) How many students do not travel by car?

Answers: 

(ii) 4

(iii) School Bus

(iv) 32

6. Given below is the data showing the number of hours spent by the students in watching television. Draw a Bar Graph for the given information.

5. The students in a school are sending Thank You cards to the soldiers at the border. Observe the graph given below.

Now answer the given questions:

(i) How many students have made less than 51 cards?

(ii) How many students have made 76 - 100 cards?

(iii) Which interval has the maximum number of students?

(iv) How many students have made more than 75 cards?

(v) How many people would you like to Thank?

Answers:

(i) 35

(ii) 15

(iii) 26 - 50

(iv) 20

6. Given below is the date showing the age of students participating in 'Poster making Competition' in school. Draw a bar graph for the given information. 

(i) maximum number of pets are dog.

(ii) Only one parrot.

(iii) Six times parrot are cats.

(iv) Two less than cats are rabbits.

(v) Double the rabbits are goats.

(vi) One less than rabbits are tortoise.

Answer:

7. Given below is the date showing the age of students participating in 'Poster making Competition' in school. Draw a bar graph for the given information. 

8. The data from the table has been used for making a bar graph to show Alexander's marks in the different subjects in a test. The maximum marks for each subject are 20.

Similar to a pictograph, a bar graph helps us to compare the information and understand it in the right manner.

Looking at the above bar graph we can say that

● Alexander got maximum marks in Painting.

● He got the minimum marks in EVS.

● He got the second highest position in Maths.

Note: Every bar graph must have a title explaining the information given in the graph and the label explaining the scales.

5th Grade Math Problems

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