List out 20 classmates' heights one by one and you get something like 148, 152, 150, 163… — looking at the raw numbers alone, it's hard to get a feel for the class's overall height distribution. But organize it into 5cm bands like "3 students in 145–150cm, 6 students in 150–155cm…" and you can see at a glance which range has the most classmates. A table organized this way — splitting data into equal-width intervals and tallying up each interval's count — is called a frequency table.
A frequency table comes with a few terms. Each interval the data is split into is called a class, and the width of that interval (say, 5cm) is called the class width. The number of data points that fall in each class is called the frequency. Draw the frequency as bars and you get a histogram — it looks similar to a bar graph, but the difference is that a histogram has no gaps between the bars, since it's dealing with continuous values that flow without any breaks (height, weight, time, and so on).
Choosing the class width turns out to be a surprisingly important decision. Split the data too finely (say, 1cm bands), and each interval ends up with just one or two data points, making the result look jagged again and hard to spot an overall trend in. Split it too coarsely (say, 50cm bands), on the other hand, and almost all the data piles into a single interval, wiping out the character of the distribution. That's why you need a feel for choosing a reasonable class width based on the amount and range of the data — as a rule of thumb, aiming for somewhere around 5 to 15 classes usually works well.
A frequency table reveals information that the average alone can't. For instance, two classes might both average exactly 70 points, yet one class could have everyone clustered between 65 and 75, while the other splits sharply between the 40s and the 90s. There's no way to tell this difference from the average alone — it only shows up once you draw a frequency table or histogram. That's why, in statistics, it matters to look at "the overall shape of how the data is spread out," not just a single summary value.
Frequency tables show up all the time in daily life — the grade distribution of test scores, the age distribution of patients at a hospital, the size-error distribution of parts produced in a factory. They appear anywhere you need to grasp a large amount of data at a glance. Even the income distribution graphs you see in the news are ultimately just frequency tables drawn as a graph.
When studying this with kids, the best approach is to actually survey your own classmates' heights, shoe sizes, or birth months and build the table yourselves. Try a large class width first, then a small one, several times, and compare how the shape of the table and histogram changes. Thinking together about "which class width shows our class's height distribution best?" also makes for a great activity.
On our activity page, you can organize 20 students' height data into a frequency table and histogram, changing the class width as you go. Press the "Survey new data" button to generate different data each time, and compare how the table and graph change with the class width.