For example,  suppose we have data related to students’ scores and need to create a distribution of students’ scores. In such a scenario, we can use the histogram and make a graphical representation of students’ scores that can easily condense the given data set, interpret, visually analyze the data points, and group them into logical ranges or bins, enabling us an organized group of data points into user-specified ranges.

What is the Histogram Formula?

The formula for the histogram revolves around the area of the bars. It is simple. It is calculated by the summation of the product of the frequency density of each class interval and the corresponding class interval’s width. The area of the histogram formula is mathematically represented as:

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Explanation of the Histogram Formula

Examples of  Histogram Formula (with Excel Template)

Let us see some simple to advanced examples to better understand the histogram equation calculation.

  • Firstly, it is to be decided on how we measure the process and what we should collect as data. Once determined, the data is gathered and presented in a tabular form, such as a spreadsheet. Now, count the number of data points gathered. Next, determine the range of the sample, which is the difference between the maximum and minimum values in the data sample. Range = Maximum value – Minimum value Next, determine the number of class intervals which can be based on either of the following two methods,As a thumb rule, use 10 as the number of intervals or-The number of intervals can be calculated by the square root of the number of data points, which is then rounded to the nearest whole number. Number of intervals = Now, determine the width of the interval class by dividing the range of the data sample by the number of intervals. Class width = Range / Number of intervals Next, develop a table or spreadsheet with frequencies for each interval. Then, derive the frequency density for each interval by dividing the frequency by the corresponding class width. Finally, the area for the histogram equation is calculated by adding the product of all the frequency density and their corresponding class width.

Range = Maximum value – Minimum value

Number of intervals =

Class width = Range / Number of intervals

Histogram Formula – Example #1

Let us consider the table below, which shows children’s weights in a class.

From the above table, we can calculate the following:

  • Class width of the first interval = 35 – 30 = 5Class width of the second interval = 45 – 35 = 10Class width of the third interval = 50 – 45 = 5Class width of the fourth interval = 55 – 50 = 5Class width of the fifth interval = 65 – 55 = 10

Again,

  • Frequency density of the first interval = 2 / 5 = 0.4Frequency density of the second interval = 7 / 10 = 0.7Frequency density of the third interval = 21 / 5 = 4.2Frequency density of the fourth interval = 15 / 5 = 3.0Frequency density of the fifth interval = 2 / 10 = 0.2

For the histogram formula calculation, we will first need to calculate class width and frequency density, as shown above.

Hence, Area of the histogram = 0.4 * 5 + 0.7 * 10 + 4.2 * 5 + 3.0 * 5 + 0.2 * 10

So, the Area of the Histogram will be –

  • Therefore, the Area of the Histogram = 47 children.

A graphical representation of the weight of children is shown below:

Relevance and Uses

The concept of a histogram equation is very useful as it portrays a set of data. Although a histogram looks quite similar to a bar chartBar ChartBar charts in excel are helpful in the representation of the single data on the horizontal bar, with categories displayed on the Y-axis and values on the X-axis. To create a bar chart, we need at least two independent and dependent variables.read more, the end-use of a histogram is very different from that of a bar chart. A histogram is useful in displaying a large amount of data in a more understandable way, which is easy to visualize. A histogram captures the frequency density of each class interval. We can determine the median and the distribution of data from a histogram. Also, the skewnessSkewnessSkewness is the deviation or degree of asymmetry shown by a bell curve or the normal distribution within a given data set. If the curve shifts to the right, it is considered positive skewness, while a curve shifted to the left represents negative skewness.read more of the distribution can be selected as if the bars on the left or the right are higher. Then, it indicates that the data is skewed, or otherwise, the data is symmetrical.

A histogram primarily finds its application in the case of large-scale exercises like a nationwide census, which may be conducted every ten years. In such cases, the data is compiled and presented in a histogram so that we can easily study it. Also, in the cases of surveys where a histogram is created, anyone who can interpret the histogram can use the data later for further studies or analysis.

This article is a guide to Histogram Formula. Here, we discuss the equation to calculate the histogram area, practical examples, and downloadable Excel templates. You may learn more about fixed income from the following articles: –

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