How to draw a histogram: From creating a frequency distribution table to differences from bar graphs and interpreting the shape of the distribution.

A histogram is a graph that divides continuous data into certain sections (classes) and shows the number (frequency) of data in each section as the height or width of the bar. Since the frequency distribution table is translated into a picture, the biggest use is that it allows you to learn the two together and shows at a glance where the data is concentrated and the shape of the distribution.

It looks similar to a bar graph, but the key difference is that there are no gaps between the bars, and the horizontal axis is a continuous number section rather than a category.

In what order do I create a frequency distribution table?

First, find the maximum and minimum values of the data, find the range, and decide how many classes to divide into. The number of classes is usually chosen between 5 and 15, but when the number of data is n, the '1+log₂n' formula proposed by Sturgis in 1926 is sometimes referred to. Next, determine the width of the classes, count the data belonging to each class, and write them down in a table.

The table above is data on the commuting time to school for 40 hypothetical students created for illustrative purposes. If you set the class boundary as 'above ~ below', there is no confusion about which box a boundary value such as 30 minutes goes. Relative frequency is the frequency divided by the total number of data, so adding them all adds up to 1.

How to distinguish between a histogram and a bar graph?

A common pitfall in testing is data such as ‘number of students by grade’. Even though grade levels are in order, a bar graph is correct because they are categories rather than continuous measurements. Conversely, data that groups measurement values into intervals, such as height or weight, is drawn as a histogram.

발표 준비는 전체 리허설 한 번만 해도 완성도가 확 올라가더라고요. 역할을 잘하는 것 위주로 나눠 본 게 저한테는 도움이 됐어요.

What can we read from the distribution shape?

When you draw a histogram, you can see whether the distribution is symmetrical, has a long tail on one side, and has one or two peaks. If the right tail is long, the mean tends to be larger than the median, so data with some large values, such as income, are reported along with the median. If there are two peaks, you can suspect the possibility of two groups with different personalities mixing together.

How the data was collected also affects the interpretation. If the sample does not evenly represent the population, the picture itself will be distorted, so it is best to check the sampling method in the survey design (Probability Sampling Wiki).

To summarize, histogram interpretation is a practice of talking about three things in order: shape, center, and spread. If you remember these three words as a sentence frame, there will be fewer elements left out in descriptive questions.

How would you do the histogram task if you tried it yourself?

For example, let's say a student in a hypothetical introductory statistics class surveyed the daily sleep hours of 30 other students in his class. If the minimum value is 4 hours and the maximum value is 9 hours, create 5 classes with a width of 1 hour, count the frequencies, add bars, and interpret the most classes and distribution shapes in two or three sentences.

• Has the class boundary been clearly defined as above/below?
• Is the sum of frequencies equal to the total number of data?
• Have the bars been drawn without gaps?
• Have the distribution shape and representative values been interpreted together?

If you change the class width and draw it twice, you can see that the same data looks different. In the interpretation, it would be good to add a line explaining why you chose the width.

This article was compiled by the Campus Down editorial department based on public data and textbook content. · Reviewed on 2026-10-25. Reference: Sturges (1926) rank number formula, basic statistics textbook, section on organizing and interpreting middle school mathematics data. Terms and classifications may differ slightly depending on the textbook and school, so match them with the expressions used in class before submitting.