Comprehensive Guide to Histograms with Illustrations

Histograms are a helpful and effective tool for organizing data, presenting information, and bridging technical and linguistic gaps because of their clear data presentation of figures, colors, and graphs, and charts. In this blog post, we will explore the definition of a histogram, the creation of a histogram, and the various kinds of histograms you can use in your presentations.

By
Visual PMP Academy
,
on
January 22, 2024

Presenting an argument is necessary when proving a point or when persuading your audience with your position, which can also be challenging. Yet, this challenge can be addressed with effective tools. The most efficient way to support your point in an argument is to deliver precise, convincing, and understandable data. To author a persuasive paper, win a bid, sign a contract, and pass an interview, you must demonstrate the appropriate figures to back up your claims. Using illustrations of varied plots and charts is quite frequent to visualize different types of data, including numbers, distributions, values, x-y connections, geospatial data, and predictions or instabilities.

This is where histograms come into the picture. Histograms are a helpful and effective tool for organizing data, presenting information, and bridging technical and linguistic gaps because of their clear data presentation of figures, colors, and graphs, and charts. We will go over the definition of a histogram, the creation of a histogram, and the various kinds of histograms in this blog.

What is a Histogram?

A histogram is a graphical representation that can show the frequency distribution of data points across a continuous range of numerical values. These numerical values are divided into bars. Generally, the width of a bar, called as bin, represents an array of numerical values. The height of a bar shows how frequently a certain data point falls inside a given bin. All bins must have the same width for visualization to be a valid histogram.

Histogram Description

A histogram is a particular type of chart that shows a graphical illustration of the distribution of data.

As with most graphs, it contains two axes:

  • the horizontal x-axis. This reflects each of the values sorted into bars or bins.
  • the vertical y-axis. This displays the frequency with which a certain set of data happens.

Here is a quick example: if a hospital is admitting patients, and we want to know the total number of patients and their ages, we can use a histogram for this purpose.

Let us go into more depth about it below.

An Example of a Histogram

First, let’s define age distribution. Age distribution is what we refer to as the subjects' relative proportions of various ages. Let’s say, for example, if a hospital admits 700 patients, and we want to know the breakdown of hospital patients by age including, the number of children, young adults, adults, senior citizens, and so on. This is where we can illustrate age distribution.

By placing all of the patients into bins with similar ages and calculating the number of patients in each bin, we may get an idea of the age distribution among the patients.

The age ranges in this example are separated into 16 successive bins. Each of these is symbolized by a vertical bar in a distinct color. The bins are then equally distributed in groups of five. Ages over 0 and up to and including 5 are placed in the first bin, those over 5 and up to and including 10 are placed in the second bin, those over 10 and up to and including 15 are placed in the third bin, and so on.

In this instance, the patient ages serve as the data points. Plotted on the y-axis, the height of each bin indicates the number of patients whose ages fall within the range of that bin. As an illustration, the histogram shows that 90 out of 700 patients are older than 45 years old and younger than or equal to 50 years old. On the contrary, ten patients are older than ten and younger than or equal to fifteen years. old.

Since histograms are created by “binning the data”, the chosen bin width determines how precise the visual representation of the data is. Before you decide on the most suitable bin width for your histogram, it is better that you experiment with different bin widths in order to ensure that the final histogram accurately reflects the underlying data.

If the bin width is too narrow, this may cause your histogram to show too many peaks and be visually cluttered, and the main trends in the data may be overlooked. If the bin width is too wide, It is possible for tiny features in the data distribution to vanish.

Illustrate Multiple Distributions Simultaneously

In a lot of situations, we need to show multiple distributions in a single display. Let's look at our sample histogram below as an example. In our histogram, we want to see the distribution of hospital patients’ ages by gender.

Let’s analyze the sample histogram: Do the number of patients generally differ in age between the sexes, or were they mostly of the same age? When we wish to see two subjects with the same two distributions, instead of creating two separate slides, we can combine two histograms for each subject, rotate them by 90 degrees, and then set the bars to point in the opposite direction of the other to create one histogram. This technique is frequently used when depicting age distributions, and the resulting graphic is typically known as an age pyramid.

Histogram Types

Different histogram types can be distinguished according on the data's frequency distribution. These types of distributions can be normal distribution, skewed distribution, bimodal distribution, multimodal distribution, and so on.  These various distribution types can be represented using a histogram.

Let’s look at each type of histogram in further detail:

Bell-Shaped Histogram: A bell-shaped histogram is one that has a noticeable "mound" in the middle with matching tapering to the left and right. What makes this shape distinct is the presence of a single mode marked by the curve's "peak”. If the shape exhibits symmetry, the values of the mean, median, and mode will be the same. It should be noted that a normally distributed data set forms a bell-shaped symmetric histogram, which gives rise to the phrase "normal distribution."

Symmetric Histogram: As the name suggests, this histogram shows symmetry. This is one in which a line drawn in the middle would divide it into two identical halves. Symmetric histograms come in two common varieties:

  • Unimodal symmetric histogram has one peak
  • Bimodal symmetric histogram has two peaks

Bimodal Histogram: A bimodal histogram is formed when the distribution shows two different peaks or modes. Each peak reflects a distinct set or classification of data that could exhibit dissimilar traits or quantities.

Uniform Histogram: A uniform histogram is one in which the frequency or number of each bin is the same. This means, there is an even or uniform distribution of values among the various bins. This signifies that the histogram has a rectangular shape and that each bin reflects an equal range of values.

Right-Skewed Histogram: On one side, a gradual tapering to the right side of the graph with a left-of-center peak characterizes a right-skewed histogram. This data set is unimodal, meaning that the mode is closer to the left side of the graph. The median and the mean of right-skewed data tapers to the right side of the graph. The mode shows a greater value than either the median or the mode. This form suggests that there is more concentration of data points than the mode, possibly outliers.

Left-Skewed Histogram: On the other side, a left-skewed histogram has gradual tapering to the left side of the graph with a right-of-center peak. This data set is also unimodal. However, in this case, the mode is closer to the right side of the graph. The mean is smaller than the median or mode and is more to the left. This form shows that the majority of outliers' have less value than the mode.

Present Multiple Distributions at the Same Time

Multiple distributions can be seen simultaneously in a variety of settings. Let us consider the weather data, for example. It may seem beneficial to visualize not just the distribution of measured temperatures within each month, but also the swings in temperature over the course of the month. This scenario requires showing a dozen temperature distributions at once, one for each month. However, this situation is not conducive to a histogram. Alternatively, there are more effective methods that you can use including ridgeline plots, boxplots, and violin plots. This is when a response variable becomes useful.

A response variable, is a concept, idea, or quantity that you mat want to measure. The response variable is the one whose distributions we want to show. Other factors can determine whether or not the response variable changes.

It is more convenient to think in terms of the response variable and one or more grouping variables whenever we are working with several distributions. Subsets of the data with unique response variable distributions are detected by the grouping variables. To understand this better, let’s take the case of temperature distributions over months, we place temperature as the response variable, while we identify the month as the grouping variable.

Box Plot: A box plot can be visualized in a standardized system. In a box plot, the presented data is divided into quartiles. Here, only the y values of the points are displayed. The box represents the top 50% of the data, and the line across the center of the boxplot indicates the median. “Whiskers” are what we call the vertical lines that emerge from the box and extend both upward and downward.

Violin Plot: Instead of using boxplots for more complex information, violins can be used. The violin plot illustrates far more comprehensive details of the data. In contrast, a boxplot will not accurately represent bimodal data on the one hand, but a violin plot can sufficiently show it. The violin plot displays only the y values of the points.

Ridgeline Plot: We can use both the box plot and violin plot to show distributions along the horizontal axis. With this data, we can now elaborate on this concept by vertically arranging the distribution plots. Because the resulting plots resemble mountain ridgelines, they are known as ridgeline plots. If you wish to display distribution trends over time, ridgeline plots are usually a good choice.

Histogram Type Examples

Some examples of various histogram types are provided below: 

  • Uniform histogram: You are probably going to observe a uniform distribution of temperatures over the range of values if you gather meteorological data, such as daily temperature readings, and then plot them in a histogram with uniform bins.
  • Bimodal histogram: If you want to analyze exam scores for a class or a population, blood pressure readings in a population, customer satisfaction ratings for a product or service, the distribution of product defects in a manufacturing process, and the visual representation of income distribution in a population, you can use a bimodal histogram.
  • Right-Skewed Histogram: Wealth and income are two well-known instances of right-skewed histograms. For example, Although the majority of people have low incomes, some millionaires and billionaires have extremely large earnings. The number of more wealthy individuals is depicted with the right tail extending into very high values. The left tail, however, cannot be smaller than zero. This circumstance results in a positive skew. Because the mean overestimates the most common numbers, you may report this as median income.
  • Left-Skewed Histogram: Although they are less common than their right-handed counterparts, left-skewed histograms do exist. They frequently happen when most scores are within the range of an upper limit where values do not exceed. A negative skew might result from values that are very distant from the peak on the lower side yet cannot surpass the cap. 

The Objective of a Histogram

A uniform histogram is used to visualize data and identify distributional biases or trends, select the appropriate number of bins for accurate data representation, compile data for statistical analysis, and modify image brightness and contrast.

Features of a Histogram

The uniform histogram is symmetrical, has an ideal number of bins, is rectangular in shape, is uniformly distributed, and lacks peaks and valleys.

When to Use a Histogram

Histograms are important to use when illustrating general distributional properties of dataset variables. You can view the approximate coordinates of the distribution’s peaks, as well as whether it is symmetric or skewed and whether any outliers exist. All we need is a variable that allows continuous numeric values to use a histogram. This indicates that, regardless of their absolute number, the differences between values are consistent.

Let's examine when each kind of histogram should be used:

  • Uniform Histogram: A uniform histogram can be used to compare different datasets with the same range of values, preliminary data for statistical analysis, illustrate randomly produced data, and modify the brightness and contrast of an image.
  • Bimodal Histogram: When displaying data that has two distinct underlying processes or sources, bimodal histograms are frequently applied. The bimodal histogram is a practical tool for group comparison, behavior analysis, subpopulation identification, and outlier detection.

The Histogram’s Common Uses

The histogram is a helpful tool for gaining a general understanding of data distribution. For example, the histogram shown above can assist decision-makers in identifying potential health risks. 

Histograms are commonly used and applied for the following purposes:

  1. Assist business owners, stakeholders, and decision-makers in identifying patterns and interpreting the significance of massive datasets.
  2. Aid stakeholders in making educated decisions by identifying trends, patterns, and irregularities from data sets.
  3. Evaluate whether process outcomes meet customer expectations.
  4. Quickly determine numerous categories to help discover each category's strengths, weaknesses, opportunities, and threats.
  5. Analyze potential process modifications or deviations at various times or schedules.
  6. Compare and evaluate the results of different processes.

 Applications of Histogram

Histograms can be used to learn about various distributions.

  • Normal Distribution: Symmetric histograms can analyze data that consists of normal distribution. You can use symmetric histograms to analyze measurement data, detect quality control deviations, analyze market trends and consumer behavior, identify trends and patterns that can inform investment decisions, identify areas for improvement, and inform process optimization decisions.
  • Bimodal Distribution: Numerous industries and purposes can benefit from the usage of bimodal histograms. Genetics, marketing, finance, industry, psychology, and education all employ bimodal histograms.

How to Create a Histogram

Analyzing enormous quantities of data across intervals can be a laborious process. Fortunately, using histograms can make this task simpler. This methodology makes trends, patterns, and anomalies visible, enabling stakeholders and project users to make well-informed decisions.

Here is a step-by-step set of instructions on making a histogram:

1. Gather Quantitative Data

First of all, gather data that you can utilize for data processing. You can do one or more of these numerous approaches to collecting data, such as brainstorming, talking to relevant people, starting focus groups, searching the internet, reading published works, and distributing surveys and questionnaires to chosen recipients.

2. Review Quantitative Data

Some data that you have gathered may not be applicable or useful to the project. That said, it must be examined in light of the project's objectives, participants, setting, and particular data acquired. Better and more accurate data that can be more useful for your histogram will be produced as a result of this approach.

3. Prepare Data

Validate that the file is in a format that is simple to import into the software that you are using. This might involve entering it into a database, framework, text document, or spreadsheet.

4. Choose a Software

Decide which software you prefer or efficient for you to use in designing your your histogram. This might be any program that can generate histograms, such as Excel, R, Python, etc.

5. Input the Data

Enter your information into the program.  This might include importing a file, copying and pasting from a spreadsheet, or utilizing a built-in function to construct a data frame, depending on the software you are using.

6. Estimate the Number of Class Intervals

Determine the number of bins, buckets, or class intervals your histogram is going to employ based on the amount and variety of the data you have prepared.

7. Calculate Class Interval Width

Determine the width of your intervals. To do this, divide your interval's maximum range by the desired number of class intervals. If, for instance, your population's ages run from 0 to 80 and you require 16 intervals, all you have to do is divide 70 by 16 to obtain a class interval width of 5 years.

8. Build Frequency Distribution Table

By using the number of data points you now have, complete your frequency distribution table to determine the height of each of your class interval bars.

9. Draft Your X and Y Axes

Draft the X and Y axes of your graph, which indicate the bins (or class intervals) and the number of data points, respectively, so that you can begin working on your histogram.

10. Draw Your Bars

Begin drawing the bars in the x and y axes using the prepared data and the computed widths and heights so that you can then finish your histogram.

Advantages and Disadvantages of Different Histogram Types

The following are some advantages and disadvantages of employing various histogram types:

Uniform Histogram

  • Advantages: The uniform histogram has several benefits. These include ease of interpretation, the ability to show how data is distributed across a range of values, assistance in determining the ideal number of bins, usefulness in preprocessing data for statistical analysis, and the ability to adjust the brightness and contrast of images.
  • Disadvantages: The uniform histogram has a few drawbacks: it depends on bin width. Therefore, it might not be good for non-uniform data, it might not be appropriate for small datasets, it can be misleading for multimodal data, and it fails to function well with outliers.

Bimodal Histogram

  • Advantages: The benefits of a bimodal histogram include its ability to effectively represent data with two distinct peaks, identify distinct subpopulations within a larger population, present insightful information about the nature of the data being analyzed, support decision-making in a broad range of cases, and detect outliers within a data set.
  • Disadvantages: There are also disadvantages to using a bimodal histogram. Due to the shape of a bimodal histogram, it can be sensitive to the bin size used to group the data, and it may not be the best representation for all data types. The disadvantages of the bimodal histogram include limited applicability to data with two distinct peaks; potential lack of insight into the underlying causes of the bimodal distribution; and interpretation that necessitates close attention to the data being analyzed.

References:

Fundamental of Data Visualization, A Primer on Making Informative and Compelling Figures, Claus O. Wilke

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