5th Grade 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.

We can also represent data pictorically with the help of a bar graph. To draw a bar graph, we need two lines-one horizontal line and the other vertical line. It also consists of vertical or horizontal bars, the length of these bars depend on the amount or quantities that are to be represented. There should be equal intervals between the numbers written on both vertical as well as on the horizontal lines. A bar graph has title and a scale. Bar graphs make it easy to compare the recorded data. Let us read a bar graph.

Definition of Bar Graph:

A bar graph is a chart with rectangular barz of equal width and length proportional to the values that they represent. The bars can be horizontal or vertical with equal spacing between them.

It is also called column group.

Each rectangle or bar represents only one value of the numerical data. So there are as many bars as the number of value in the numerical data. The height or length of a bar indicates on a suitable scale the corresponding value of the numerical data

Scale of a Bar Graph:

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.

Reading and Interpreting a Bar Graph:

To read a bar graph, we proceed as per the following steps:

Step I: Know what it represents or what is the information given by it. For this, we read captions which are generally written just below the horizontal line and adjacen vertical line.

Step II: After knowing what does a bar graph represent, we read the scale so that we know the precise values in the given data.

After reading a bar graph one must be able to draw certain conclusions from it. Drawing some conclusions from given bar graph means interpretations of the bar graph.

Construction of Bar Graphs:

Step I: On a graph paper, we draw-horizontal line (x-axis) and a vertical line y-axis.

Step II: Mark points at equal intervals along horizontal line, below these points write the names of the data items whose values are to be plotted.

Step III: Choose the suitable scale. On the scale determine the height of the bars for the numerical values.

Step IV: Mark these heights parallel to the y-axis from the points taken in Step II.

Step V: On the horizontal line, draw bars of equal width for the heights marked in step IV.

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.

2. The following graph shows the number of students in each class of a school Study the graph and answer the questions that follow:

(i) How many students are there in class I?

(ii) How many more students are there in class IV than in class III?

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

(iv) What is the difference between the maximum and the minimum number of students?

Solution:

(i) Number of students in class I is 20.

(ii) Number of students in class IV more than that in Class III = 100 - 80 = 20

(iii) Class IV has maximum number of students.

(iv) Class IV has the maximum number of students, i.e., 100, and Class I has the minimum number of students, i.e., 20.

So, the difference between these two = 100 - 20 = 80.

3. Read the given bar graph which shows sale of trousers in a ready-made shop and answer the following questions:

(i) What information is given by the bar graph?

(ii) Mention the scale chosen on the horizontal line representing number of trousers.

(iii) Mention the day of maximum sale.

(iv) Mention the day of minimum sale.

(v) How many trousers sold on Wednesday was the same number of trousers sold on Saturday?

Solution:

(i) The given bar graph shows the sale of trousers in a ready made garments shop from Monday to Saturday.

(ii) The scale chosen is 1 unit = 5 trousers.

(iii) On Friday, maximum number of trousers were sold.

(iv) On Monday, minimum number of trousers were sold.

(v) On Wednesday, 40 trousers were sold, Yes, on Saturday same number of trousers were sold.

Worksheet 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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