Frequency tables, bar charts and pie charts

Some data sets are too big for a simple list, so we group the values into ranges called intervals. A histogram is a chart of those groups. It looks like a bar chart, but the bars touch each other, because each bar covers a range of numbers, like 10 to 19, instead of one named group.

To build a histogram, count how many values fall into each interval, then draw one bar per interval. The height of each bar shows the count, and you can spot the busiest interval right away.

A frequency polygon is another way to show the same table. Plot a dot at the top middle of each bar, then join the dots with straight lines. This line chart is handy when you compare two grouped data sets on the same grid, because two lines sit side by side more easily than two sets of bars.

Choose your intervals with care. They should all be the same width, cover every value, and not overlap. About 5 to 10 intervals works well for most school data.

Ask some classmates how many movies they watched at the theater last month. You will get a jumble of numbers like 2, 0, 3, 1, 1, 4. Raw data like this is hard to read on its own.

First, make a frequency table. List each possible answer in one column, then tally how many people gave each answer. Now the jumble becomes a neat table you can count at a glance.

You can go one step further with a relative frequency table. Instead of the count, each row shows the share of the group, like 4 out of 20 people, which you can also write as a fraction or a percent. Relative frequencies help when you compare groups of different sizes, like one class of 20 with one class of 25.

Try grouping the same answers in different ways, such as exact counts versus ranges like 0 to 1 and 2 or more. The totals stay the same, but the story can look different. That is why choosing sensible groups matters when you build a table.

Before you pick a chart, look at what kind of data you have. Categorical data sorts things into groups with names, like favorite color or type of pet. Quantitative data is a number that measures something, like height, score, or minutes.

A frequency distribution is a table that counts how many items fall into each group or range. It is the first step for almost every chart you will draw, because the chart is just a picture of the counts in your table.

The type of data tells you which picture works best. Categorical data likes bar charts and pie charts, where each bar or slice stands for one named group. Quantitative data grouped into ranges likes histograms and frequency polygons, because the bars touch to show the numbers run into each other.

Get the table right first, with clear headings and honest counts. Then let the chart do the showing. A good chart makes one big idea obvious, like which group is largest or where most of the values bunch up.

Frequency means how many times a value appears in your data set. If three children chose red, the frequency of red is 3.

A frequency table is a table of grouped data shown next to its frequencies. Each row names a group or a range, and the number beside it says how many items belong there.

A histogram is a chart of a frequency table for numbers. Its bars touch, because the ranges run into each other, like 0 to 9 then 10 to 19.

A frequency polygon looks like a line graph. You plot a point at the middle of the top of each bar and join the points with straight lines. It is great for comparing two grouped data sets on one grid.

A pie chart is a circle split into slices. Each slice angle matches the group's share of the total, so big groups get wide slices.

A pictogram uses small pictures to stand for amounts. Pick one symbol to mean a fixed amount, and always include a key that says what the symbol counts.