Histogram Questions with Solutions

Histogram is the graphical representation of frequency distribution in Statistics. It is a two dimensional diagram which represents class interval and various frequencies with respect to different class intervals. It is useful to check the shape of the data distribution. It is an important concept in the fields of statistics and mathematics. In this article, we will discuss histogram, its formula, and the solved questions & answers related to it.

Histogram is a graphical or visual representation of numerical data. It is a set of rectangles adjacent to each other. Each rectangle or bar represents a particular range of data or value. A histogram is a two-dimensional diagram, where the X axis shows the class intervals and the Y axis represents various frequencies with respect to different class intervals. In statistics, frequency is the repetition of numerical data. When these numerals are written in the form of a table, it is called frequency distribution. These frequency distributions can be represented in the form of graphics, one of which is a histogram. It is an integral part of statistics and mathematics. It is used to check the distributions of numerical data, changes of data from one point to another, and, most importantly , to analyze whether this process meets customer requirements or not.

Histogram of frequency distribution can be divided into two parts,

• Histogram of equal class intervals.
• Histogram of unequal class intervals.

The histogram formula for frequency distributions is:

Frequency density of any class = Given frequency/ Adjustment factor

where,

• Adjustment factor of any class = class interval of that class / lowest class interval

Here are some questions and solutions related to Histogram discussed below:

Q1. Draw a histogram for the following data distribution:

Solution:

The Histogram can be drawn as:

Q2. A frequency table is given below:

Answer the following questions:

1. What is the total data points?

2. Find out which interval has the highest frequency.

3. Which interval has the lowest frequency?

Solution:

1. Total data points = sum of all the frequencies. Hence the total data points will be = 10+15+5+20 = 50.

2. The interval (30-40) has the highest frequency of 20.

3. The interval (20-30) has the lowest frequency of 5.

Q3. A following data set has been given: { 12, 14, 10, 13, 16, 18, 17, 15, 21, 11, 20, 23, 25}

1. Determine appropriate intervals and frequencies.

2. Construct a frequency distribution table.

Solution:

1. The appropriate intervals with frequencies are:

Interval : Frequency

• 10-15 : 6
• 15-20 : 5
• 20-25 : 4

2. The frequency table is:

Q4. The below histogram shows the weekly wages of workers at a construction site:

Answer the following questions:

1. How many workers get wages of ₹ 500-600?

2. Construct a frequency distribution table.

3. What is the cumulative frequency for the class 400-500?

Solution:

1. 150 workers get wages of ₹ 500-600.

2. The frequency distribution table is:

3. The cumulative frequency for the class 400-500 is = 200+300 = 500.

Q5. Study the given histogram:

1. Prepare a cumulative frequency distribution table for the above histogram.

2. Which interval has the maximum frequency?

Solution:

1. The Cumulative distribution table is:

2. The interval (40-50) has the maximum frequency of 50.

Q6: Draw a histogram for the following data distribution:

Solution:

The Histogram can be drawn as:

Q7. Draw a histogram for the following data distribution:

Solution:

The histogram is shown as

Q8. Study the comparison of a test result between class A and class B

Class A

Class B

Which class performed better in the test? Answer with explanation.

Solution:

To determine which class performed better we can compare the number of students in the higher score intervals.

For, Class A

From (80-90), students = 15

From (90-100), students = 2

Total = 17

for, Class B

From (80-90), students = 12

From (90-100), students = 8

Total = 20

Therefore, Class B has performed better as it has more number of students in the higher score intervals than Class A.

Q9. Study the table and draw a histogram on these information :

Solution:

The histogram for the above data is shown below:

Q1. Draw a histogram for the following frequency distribution:

Also answer the following questions:

1. What is the highest class interval?

2. What is the adjustment factor of the class interval (15-25) ?

Q2. The annual amount of rainfall for 22 cities was recorded and is shown in the table:

Answer the following question:

1. How many cities could have an annual rainfall of 30 in – 32.5 in ?

2. Draw a histogram.

Q3. The following data shows the number of cameras sold everyday. Look at the table and make a histogram.

Q4. The following data shows the height of 100 players. Read the data and draw a histogram.

For what reason is a histogram most useful?

A histogram is a graphical representation of the frequency distribution of continuous series using rectangles. So, it is good for showing general distribution of given data .

What is obtained from histogram?

Histogram is useful to check the shape of the data distribution. It is used to check whether the process changes from one period to another, to determine whether the output is different when it involves two or more processes. Most importantly to analyse whether the given process meets the customer requirement.

Can a histogram have gaps?

Some histograms have a gap. It occurs between two bars where there are no data provided or the data is 0.

What is a histogram also known as?

Histogram is also known as Frequency distribution. A histogram is a graphical representation in which values are plotted on the horizontal axis, and their density is plotted on the vertical axis.

Who invented the histogram?

Histogram was first introduced by Karl Pearson. It is an approximate representation of the distribution of numerical data.

What is bin in histogram?

The towers or bars of a histogram are called bins. Each bin represents a particular value or data range.

What is bin size in a histogram?

The height of each bin shows how many values from the data fall into that range. Width of each bin = (max value of data – min value of data) / total number of bins. The default value of the number of bins to be created in a histogram is 10.