Histogram: Difference Between Histogram and Bar Graph and Histogram Types

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Statistics is a stream of mathematics that is applied in various fields. The numerals are repeated in statistical data. This repetition is known as Frequency which can be written in the form of a table, called frequency distribution. A Frequency distribution can be shown graphically by using different types of graphs and Histogram is one among them.

What is Histogram?

A histogram is an area diagram. It can be defined as a set of rectangles with bases along with the intervals between class boundaries and with areas proportional to frequencies in the corresponding classes. In such representations, all the rectangles are adjacent since the base covers the intervals between class boundaries. The heights of rectangles are proportional to corresponding frequencies of similar classes and for different classes, the heights will be proportional to corresponding frequency densities.

Diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval.

How to Make Histogram?

You need to follow the below steps to construct a histogram.

  1. Begin by marking the class intervals on X-axis and Frequencies on Y-axis.

  2. The scales for both the axes have to be same.

  3. Class intervals need to be exclusive.

  4. Draw rectangles with bases as class intervals and corresponding frequencies as heights.

  5. A rectangle is built on each class interval since the class limits are marked on the horizontal axis, and the frequencies are indicated on the vertical axis.

  6. The height of each rectangle is proportional to the corresponding class frequency if the intervals are equal.

  7. The area of every individual rectangle is proportional to the corresponding class frequency if the intervals are unequal.

Although histograms seem similar to graphs, there is a slight difference between them. The histogram does not involve any gaps between the two successive bars.

Difference between Histogram and Bar Graph

The difference between the histogram and the bar graph is given below:

Difference Between Histogram and Bar Graph

Histogram

Bar Graph

It is two – dimensional figure

It is a one – dimensional figure

The frequency is shown by the area of each rectangle

The height shows the frequency and the width has no significance.

It shows rectangles touching each other

It consists of rectangles separated from each other with equal spaces.

Histogram Types

The following are the different types:

Uniform Histogram

A uniform distribution reveals that the number of classes is too small, and each class has the same number of elements. It may involve distribution that has several peaks.

Uniform Histogram

Uniform Histogram

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Bimodal Histogram

If a histogram has two peaks, it is said to be bimodal. Bimodality occurs when the data set has observations on two different kinds of individuals or combined groups if the centres of the two separate histograms are far enough to the variability in both the data sets.

Bimodal Histogram

Bimodal Histogram

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Symmetric Histogram

When you draw the vertical line down the center of the histogram, and the two sides are identical in size and shape, the histogram is said to be symmetric. The diagram is perfectly symmetric if the right half portion of the image is exactly identical to the left half. The histograms that are not symmetric are known as skewed.

Symmetric Histogram

Symmetric Histogram

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Probability Histogram

A Probability Histogram shows a pictorial representation of a discrete probability distribution. It consists of a rectangle centered on every value of x, and the area of each rectangle is proportional to the probability of the corresponding value. The probability histogram diagram is begun by selecting the classes. The probabilities of each outcome are the heights of the bars of the histogram.

Probability Histogram

Probability Histogram

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Example 1: The histogram for a frequency distribution is given below.

Probability Histogram

Probability Histogram

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Q. 1 What is the frequency of the class interval 15 – 20?

Solution:

As we can see the histogram graph,

Class interval 15 – 20 has a frequency 25 (in image red color bar show the interval 15 - 20)

Q. 2 What is the class intervals having the greatest frequency?

Solution:

As shown in figure,

The bar is largest of interval 20 – 25 (in image green color bar is largest and its class interval 20 -25)

Q. 3 Construct a short – frequency table of the distribution.

Solution:

We have constructed below the short frequency table.

Construct a short – frequency table of the distribution

Class Interval

Frequency

10 -15

20

15 – 20

25

20 – 25

30

25 – 30

15

30 – 35

10

35 – 40

5

Q. 4 Construct a cumulative frequency table of the distribution.

Solution:

We have constructed below a cumulative frequency table.

Construct a cumulative frequency table of the distribution

Class Interval

Frequency

Cumulative Frequency

10 -15

20

20

15 – 20

25

45

20 – 25

30

75

25 – 30

15

90

30 – 35

10

100

35 – 40

5

105