Histogram Questions with Solutions

To understand histograms well, practice is very important. Here, you’ll find questions with answers to help you learn how to read and work with histograms step by step.

In statistics, a histogram is a type of bar graph used to show how often data appears within certain ranges. It’s mostly used for continuous data, meaning numbers that can take any value in a given range.

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Unlike regular bar graphs, histograms have no gaps between the bars, showing that the data flows without breaks. This makes them perfect for showing how values are grouped into intervals.

Key Points to Remember About Histograms:

Histograms are used to display continuous (non-stop) data.
Bars touch each other—there are no spaces in between.
The height of each bar shows how many times a value appears (called frequency).
The width of each bar shows the size of the interval or group.
Always start your graph from zero, and use equal intervals unless noted.
If the graph skips some numbers at the beginning, a small zig-zag line is drawn on the axis to show the break.
When all intervals are the same size, the area of each bar matches the frequency.

Discover more about histograms and how to create one by visiting this page.

Let's dive into some questions related to plotting and interpreting histograms.

Example 1: Data Table

Interval	Frequency
0–10	8
10–20	12
20–30	18
30–40	7

Questions:

What is the total number of data points?
Which interval has the highest frequency?
Which interval has the lowest frequency?

Solution:

Total = 8 + 12 + 18 + 7 = 45
Highest frequency = 20–30 interval
Lowest frequency = 30–40 interval

Example 2: Test Score Distribution

Marks	Students
40–50	5
50–60	10
60–70	8
70–80	12

Question: How many students scored 60 or more?
Answer: 8 + 12 = 20 students

Example 3: Frequency Table

Class Interval	Frequency
5–15	6
15–25	11
25–35	9
35–45	4

Question: What is the cumulative frequency of class 25–35?
Answer : 6 + 11 + 9 = 26

Example 4: Histogram-Based Attendance

Age Group	People
0–10	4
10–20	8
20–30	15
30–40	10
40–50	3

Question: How many people are younger than 30?
Answer: 4 + 8 + 15 = 27

Example 5: Employee Salary Ranges

Salary Range (₹)	Employees
10000–15000	7
15000–20000	13
20000–25000	10
25000–30000	5

Question: How many employees earn less than ₹25,000?
Answer: 7 + 13 + 10 = 30

Example 6: Height of Boys

Height (cm)	Boys
130–140	5
140–150	9
150–160	12
160–170	4

Question: Which class has the highest frequency?
Answer: 150–160 (12 boys)

Example 7:Response Time (seconds)

Given data: {15, 20, 22, 24, 28, 32, 34, 36, 38, 40, 42, 45}

Group into class intervals:

Interval	Frequency
15–25	4
25–35	3
35–45	4
45–55	1

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FAQs For Histogram Questions with Solutions

What is a histogram in statistics?

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.

What is the difference between a bar graph and a histogram?

A bar graph is made by keeping uniform gaps in between the rectangular bars, whereas in a histogram, there are no gaps. This is to show the continuity of the data.

What does the height of the bars in a histogram represent?

The height of the bars in a histogram represents the frequency of the data point, whereas the width represents the length of the class or interval.

How do you read a histogram?

Each bar represents how many values fall within a certain range. The height of the bar shows the frequency. Look at the x-axis for the data intervals and the y-axis for how often the data occurs.

What are the key parts of a histogram?

X-axis: Data intervals or classes Y-axis: Frequency (number of times values fall into the interval) Bars: Height represents how many values are in that range