#### Solved Examples and Worksheet for Constructing Histograms

Q1The number of hours each student of a class spends for studies are 8, 4, 5, 7, 4, 6, 9, 7, 6 and 5 hours. Pick the histogram that represents the data correctly.

A. Graph 3
B. Graph 4
C. Graph 2
D. Graph 1

Step: 1
The bars in the histogram indicate the number of students who study for the particular number of hours.
Step: 2
From the data, the number of students who study for 4 to 5 hours is 4.
[There are 4 numbers in the range of 4 to 5.]
Step: 3
The number of students who study for 6 to 7 hours is 4.
[There are 4 numbers in the range of 6 to 7.]
Step: 4
The number of students who study for 8 to 9 hours is 2.
[There are 2 numbers in the range 8 to 9.]
Step: 5
The histogram in Graph 2 has bars of heights 4, 4 and 2.
Step: 6
So, the histogram shown in Graph 2 represents the data correctly.
Correct Answer is :   Graph 2
Q2The scores of 20 students in a quiz are collected and shown in the table: Construct a frequency distribution and a histogram for the data.

A. Figure - A
B. Figure - B

Step: 1
[Frequency distribution and Histogram.]

Correct Answer is :   Figure - A
Q3A survey of 50 clothing stores reported these number of sales held during a randomly selected month. Select the correct histogram representing the data shown.
 Number of sales Frequency 11 - 15 5 16 - 20 7 21 - 25 17 26 - 30 10 31 - 35 3 36 - 40 8

A. Graph 1 only
B. both Graph 1 and Graph 2
C. Graph 2 only
D. neither Graph 1 nor Graph 2

Step: 1
Class boundaries of each class (number of sales) are shown in the frequency distribution.
Step: 2
Represent the frequency on the y - axis and the class boundaries on the x - axis.
Step: 3

Step: 4
So, Graph 1 represents the histogram for the data.
Correct Answer is :   Graph 1 only
Q4The table represents the number of vehicles that go in a particular route during different times in a day. Which of the histograms represents the data correctly?
 Hours Number of vehicles (in thousands) 0 - 6 1.5 7 - 12 2.5 13 - 18 1.5 19 - 24 1

A. Graph 3
B. Graph 4
C. Graph 2
D. Graph 1

Step: 1
The heights of the bars in the histograms indicate the number of vehicles that go in the route in a particular interval of time in a day.
Step: 2
Observe the heights of the bars in the histograms to match with the values given in the table.
Step: 3
It can be observed that the heights of the bars in histogram of Graph 4 exactly match with the data in the table.
Step: 4
So, the histogram in Graph 4 represents the data given in the table correctly.
Correct Answer is :   Graph 4
Q5The discounts offered by a super market are shown in the table. Which of the histograms is the correct representation of the data?
 Amount (in $) Discount% 1000 - 1999 1 2000 - 2999 2 3000 - 3999 4 4000 - 4999 8 5000 - 5999 10 A. Graph 4 B. Graph 3 C. Graph 2 D. Graph 1 Step: 1 The heights of the bars in the histogram indicate the discount offered (in %) for the corresponding amount (in$).
Step: 2
Match the heights of the bars in each graph with the values in the table.
Step: 3
It can be observed that the heights of the bars in Graph 3 match with the values in the table.
Step: 4
So, Graph 3 is the correct representation of the data.
Correct Answer is :   Graph 3
Q6The frequency distribution of points scored by 10 students in a quiz competition is given in the table. Identify the histogram that represents the data correctly.
 Points scored Frequency (f) 0 - 4 1 5 - 9 5 10 - 14 3 15 - 19 1

A. Graph - 1
B. Graph - 3
C. Graph - 2
D. Graph - 4

Step: 1
First, find the midpoint of each class using the formula,
Midpoint of a class, x = lower limit + upper limit2
[Formula.]

Step: 2
From the table, the points scored is represented along the horizontal axis and the respective frequency along the vertical axis. The height of each rectangle represents the frequency of the corresponding class.
Step: 3
Observe the histograms to match the plotted points with the values given in the table.
Step: 4
Among the graphs, Graph 2 is the correct representation of the table.
Correct Answer is :   Graph - 2
Q7The number of hours each student of a class spends for studies are 8, 4, 5, 7, 4, 6, 9, 7, 6 and 5 hours. Choose the histogram that represents the data correctly.

A. Graph 1
B. Graph 3
C. Graph 2
D. Graph 4

Step: 1
The bars in the histogram indicate the number of students who study for the particular number of hours.
Step: 2
From the data, the number of students who study for 4 to 5 hours is 4.
[There are 4 numbers in the range of 4 to 5.]
Step: 3
The number of students who study for 6 to 7 hours is 4.
[There are 4 numbers in the range of 6 to 7.]
Step: 4
The number of students who study for 8 to 9 hours is 2.
[There are 2 numbers in the range 8 to 9.]
Step: 5
The histogram in Graph 2 has bars of heights 4, 4 and 2.
Step: 6
So, the histogram shown in Graph 2 represents the data correctly.
Correct Answer is :   Graph 2
Q8Which of the histograms represents the data correctly?
 Class-interval Frequency 5 - 10 2 10 - 15 2.5 15- 20 1.5 20- 25 1

A. Figure 1
B. Figure 3
C. Figure 2
D. Figure 4

Step: 1
Take class-interval along the x-axis and frequency along y-axis.
Step: 2
Along y-axis, mark equal intervals of 0.5.
Step: 3
Along x-axis, mark equal intervals of 5.
Step: 4
Draw rectangles with bases 5 - 10, 10 - 15, 15 - 20 and 20 - 25 of heights 2, 2.5, 1.5 and 1 respectively.
Step: 5
The graph obtained is as follows.
Step: 6
So, the histogram in Figure 2 represents the data given in the table correctly.
Correct Answer is :   Figure 2
Q9Which of the graphs best represents the data?
 Class-interval Frequency 50-60 2 60-70 3 70-80 5 80-90 5

A. Graph 1
B. Graph 2
C. Graph 4
D. Graph 3

Step: 1
Take class-interval along the x-axis and frequency along y-axis.
Step: 2
Along y-axis, mark equal intervals of 1.
Step: 3
Along x-axis, start from 50 and mark equal intervals of 10.
Step: 4
Draw rectangles with bases 50 - 60, 60 - 70, 70 - 80 and 80 - 90 of heights 2, 3, 5 and 5 respectively.
Step: 5
Since the scale on x-axis starts at 50, make a kink in the beginning.
Step: 6
The graph obtained is as follows.
Step: 7
Therefore, Graph 3 represents the data correctly.
Correct Answer is :   Graph 3
Q10The table represents the temperature inside a Snow Park with respect to hours. Which of the histograms represents the data correctly?
 Hours Temperature in Celsius 50-60 2.5 60-70 4 70-80 5 80-90 3

A. Graph 3
B. Graph 4
C. Graph 2
D. Graph 1

Step: 1
Take class-interval along the x-axis and frequency along y-axis.
Step: 2
Along y-axis, mark equal intervals of 1.
Step: 3
Along x-axis, start from 50 and mark equal intervals of 10.
Step: 4
Draw rectangles with bases 50 - 60, 60 - 70, 70 - 80 and 80 - 90 of heights 2.5, 4, 5 and 3 respectively.
Step: 5
Since the scale on x-axis starts at 50, make a kink in the beginning.
Step: 6
The graph obtained is as follows.
Step: 7
So, the histogram in Graph 4 represents the data given in the table correctly.
Correct Answer is :   Graph 4
Q11The heights of girls of a class are given in the table. Pick the histogram which represents the data.
 Height (in cm) Number of girls 140-145 20 145-150 15 150-155 10 155-160 15

A. Figure 1
B. Figure 4
C. Figure 3
D. Figure 2

Step: 1
Take height of the girls along x-axis and the number of girls along the y-axis.
Step: 2
Along y-axis, mark equal intervals of 5.
Step: 3
Along x-axis, start from 140 and mark equal intervals of 5.
Step: 4
Draw rectangles with bases 140-145, 145-150, 150-155 and 155-160 and heights 20, 15, 10 and 15 respectively.
Step: 5
Since the scale on x-axis starts at 140, make a kink in the beginning.
Step: 6
The graph obtained is as follows.
Step: 7
Therefore, the histogram in Figure 3 represents the data correctly.
Correct Answer is :   Figure 3
Q12The following table represents a random survey of 80 cars for the fuel efficiency, as measured in miles per gallon. Which of the histograms is the correct representation of the data?
 Fuel efficiency (miles per gallon) 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 Number of cars 2 16 28 20 8 4 2

A. Graph 3
B. Graph 2
C. Graph 4
D. Graph 1

Step: 1
Take Fuel Effieciency (miles per gallon) along x - axis and Number of cars along y- axis.
Step: 2
Along x - axis mark the numbers as 5, 10, 15, 20, 25, 30, 35, 40 and 45.
Step: 3
Along y - axis mark the numbers as 4, 8, 12, 16, 20, 24, 28 and 32.
Step: 4
Draw rectangles with bases 10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35, 35 - 40 and 40 - 45 of heights 2, 16, 28, 20, 8, 4 and 2 respectively.
Step: 5
The graph obtained is as follows:
Step: 6

Step: 7
So, the histogram in Graph 3 represents the data given in the table accurately.
Correct Answer is :   Graph 3
• Data