Histogram Questions

Histogram questions with solutions are provided for students to practise and learn how to interpret histograms. In statistics, a histogram represents a continuous frequency data distribution, whether grouped or ungrouped. By presenting data using a histogram, we represent data points within a particular range or interval. A histogram looks similar to that of a bar graph; the main difference between both of them is that a bar graph is made by keeping uniform gaps in between the rectangular bars, whereas in a histogram, there are no gaps.

Some important facts about histograms:

• Histograms represent a continuous form of data.
• Bars are made with no gaps in between them to show the continuity of the data.
• The height of the bars represents the frequency of the data point, whereas the width represents the length of the class or interval.
• It is required that the calibrations on axes should begin with zero keeping equal intervals. Sometimes, we use a kink or a zig-zag line to show a break in the axes.
• If the chosen class intervals are uniform, then the area of bars directly varies according to the frequency of the class interval.

Learn more facts about histograms and how to make a histogram.

Video Lesson on Histograms

Histograms Questions with Solutions

Let us practice some questions related to plotting and interpreting histograms.

Question 1:

The below histogram shows the weekly wages of workers at a construction site:

Answer the following questions:

(i) How many workers get wages of ₹ 60-70?

(ii) Construct a frequency distribution table.

(iii) What is the cumulative frequency for the class 50-60?

Solution:

(i) 16 workers

(ii)

(iii) The cumulative frequency for the class 50-60 = 10 + 20 + 40 = 70.

Question 2:

Study the given histogram:

Answer the following questions:

(i) Prepare a cumulative frequency distribution table for the above histogram.

(ii) Which class interval has the maximum frequency?

(iii) Which class interval has the minimum frequency?

Solution:

(i)

(ii) 10-20 class interval has the maximum frequency.

(ii) 30-40 class interval has the minimum frequency.

Question 3:

The following histogram shows the height of students within a class:

Answer the following questions:

(i) How many students have a height of less than 140 cm?

(ii) How many students have a height greater than 140 cm but less than 155 cm?

Solution:

(i) Number of students having height less than 140 cm = 6 + 8 + 20 = 34

(ii) Number of students having height greater than 140 cm but less than 155 cm = 18 + 16 = 34.

Question 4:

Study the following histogram and answer the questions given below:

(i) How many students scored below 60%?

(ii) How many students scored above 80%?

Solution:

(i) Number of students who have scored below 60% = 3 + 2 + 5 = 10

(ii) Number of students who have scored above 80% = 12

Question 5:

The following histogram shows the data regarding the number of people from different age groups who visited to watch an animated movie in a day.

Answer the following questions:

(i) How many people under 20 years of age visited the theatre?

(ii) How many people over 40 years of age visited the theatre?

Solution:

(i) Number of people under 20 years of age who have visited the theatre = 80 + 140 = 220.

(ii) Number of people over 40 years of age who have visited the theatre = 20.

Also Read:

• Pie Charts
• Bar Graphs
• Frequency Polygon
• Cumulative Frequency Curve

Question 6:

Draw a histogram for the following data distribution:

Solution:

The histogram can be plotted as:

Question 7:

Draw a histogram for the following data distribution:

Solution:

The histogram can be plotted as:

Question 8:

Draw a histogram for the following data distribution:

Solution:

The histogram can be plotted as:

Question 9:

Draw a histogram for the following data distribution:

Solution:

The histogram can be plotted as:

Question 10:

The time taken (in seconds) by 25 students to solve a problem was:

17, 20, 24, 26, 27, 30, 38, 34, 40, 35, 47, 41, 44, 49, 45, 48, 44, 54, 50, 60, 58, 58, 63, 55, 20.

Solution:

Let us make a grouped frequency table for the given data:

The histogram can be plotted as:

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Practice Questions on Histograms

1. Draw a histogram for the following data distribution:

2. Draw a histogram to show the data for rainfall in Madhya Pradesh from 2012 to 2019.

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