Introduction

Statistics provides a wide range of tools for understanding and visualizing data. One of the most fundamental and useful tools is the histogram, which offers a graphical representation of the distribution of a continuous dataset. Through this visualization, we can identify patterns, understand the shape of the distribution, such as whether it is symmetrical, normal, or skewed, detect outliers, and generally gain a comprehensive view of the structure of our data.

What is a histogram?

A histogram is a graphical representation of frequencies. It displays data through rectangular bars, where each bar represents an interval of values, also called a class. The horizontal axis corresponds to the scale of the continuous variable, while the vertical axis expresses the frequency or frequency density. In this way, we can immediately understand how often observations occur in specific ranges of the variable. The usefulness of the histogram lies in the fact that it reveals the underlying distribution of the data. For example, we can examine whether a variable, such as age, follows a normal distribution or whether it shows skewness to the right or to the left. This is extremely important in data analysis, since many statistical methods rely on assumptions regarding the type of distribution.

How is a histogram created?

The process of creating a histogram begins with dividing the data into intervals, called classes or bins. These intervals must be continuous and cover the entire range of the dataset. For example, if we study the age of a population, we can divide the data into categories of ten years each, such as 20–29, 30–39, 40–49, and so forth. Next, we count the number of observations that belong to each interval. This frequency count is represented with a bar, whose area, and not just its height, expresses the total number of observations contained in the interval. The height of the bar depends on the width of the interval, and the larger the interval, the smaller the height may be, so that the area remains representative of the frequency. It is important to note that in many cases histograms use intervals of equal width. This makes the bar heights proportional to the frequencies and therefore easier to interpret. However, when the intervals have different widths, the visual analysis must be based on the area of each bar and not its height.

Histogram and the area of bars

A common mistake in interpreting histograms is the confusion between height and area. The area of each bar represents the frequency, meaning the number of observations. When all intervals have the same width, the height indeed reflects the frequency as well. However, in cases of unequal intervals, the height alone is not sufficient, and we need to take the width into account to understand the frequency correctly. This detail is particularly important in more advanced analyses, where data are not evenly distributed, and researchers choose intervals of different sizes in order to better highlight the structure of the observations.

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

Although histograms and bar charts look visually similar, the two types of graphs have different purposes and meanings. The histogram is used exclusively for continuous data, which are divided into intervals. It shows the frequency of values within those intervals, and its bars are continuous, with no gaps, symbolizing the uninterrupted nature of the variable. The bar chart, on the other hand, is used for categorical or discrete data. In this case, each bar represents a category, such as gender, occupation, or color preference. The bars in a bar chart are separate, with visible gaps between them, emphasizing the discrete nature of the categories. This difference is fundamental, since the histogram aims to reveal the distribution of a continuous variable, while the bar chart aims to compare magnitudes among categories.

Conclusion

The histogram is one of the most essential tools for data analysis and visualization. Through it, we can understand the distribution of a continuous variable, identify patterns and outliers, and make decisions about further statistical analyses. Correct understanding of the concept of area, and not only bar height, is critical for accurate interpretation of a histogram. Furthermore, it is important to distinguish the histogram from the bar chart, so that each graphical method is used in the proper context. The histogram is used for continuous variables, while the bar chart is used for categorical or discrete variables. In this way, we achieve an accurate and meaningful representation of our data.