Bar Charts and Pictograms

Picturing frequencies

Which fruit does your class like best? Which colour of car passes the school gate most often? Survey results like these turn up everywhere — on classroom posters, in science projects, in newspapers — and they are almost always shown as a bar chart or a pictogram rather than a plain list of numbers.

A frequency table is a list of numbers — how many children like each fruit, how many cars passed each colour. A chart turns those numbers into a picture you can read at a glance: you can spot the biggest, the smallest, and the gaps without doing any sums.

A bar chart draws each category as a bar. Every bar is the same width with a gap between it and the next, and its height — read off the labelled axis — gives that category's frequency. The rule is simple: taller bar, bigger count. The tallest bar is the most common category; the shortest is the least common.

A pictogram uses a picture instead of a bar. A key tells you how many each picture is worth — for example \text{🙂} = 5 — so three pictures mean 3 \times 5 = 15. A part-picture (half a face, say) shows a part of that number, so half a symbol here would mean 2.5.

The table has every exact number, but your eyes have to read and compare them one by one. A chart does the comparing for you: the tallest bar simply looks tallest, so "which is most popular?" is answered in a single glance. That is the whole point of a chart — it trades a little exactness for a lot of speed.

Reading a bar chart

Step through this one: first the frequency axis with its ticks, then a bar for each of four categories A, B, C, D — heights 3, 5, 8 and 4.

Worked example. Reading off the chart above:

To read any bar, slide your finger from its top straight across to the axis and read the number there. If the top sits between two ticks, count the small squares to land on the exact value.

Pictograms: one picture, many things

A pictogram swaps bars for pictures. Because drawing 30 pizzas would take forever, one picture usually stands for several items — and the key tells you how many. To read a row you multiply the number of pictures by the key, then add on any part-picture.

Worked example. A shop records pizzas sold, with the key \text{🍕} = 10:

A class voted for their favourite pet. Here each picture stands for 2 children (that's the key). Count the pictures in a row, then double it.

Cat  cat cat cat cat  = 8
Dog  dog dog dog  = 6
Duck duck duck duck duck duck  = 10
Fish  fish fish  = 4

The duck row is longest, so ducks are the most popular with 5 \times 2 = 10 votes. Altogether 8 + 6 + 10 + 4 = 28 children voted.

Cookies eaten at the party, with the key \text{🍪} = 4. Notice the last picture in the Tuesday row is only half a cookie — a part-picture worth half of 4, which is 2.

Mon  cookie cookie cookie  = 12
Tue  cookie cookie half a cookie  = 10

Tuesday is 2 \times 4 + 2 = 10 cookies — two whole pictures plus the half. A part-picture is the pictogram's clever way of showing a number that is not a neat multiple of the key.

Watch the scale, watch the key

Most mistakes with charts are not sums gone wrong — they are misreadings. Two traps catch nearly everyone:

Try it: a chart that changes

Here is a fresh survey of four fruits, with the votes counted up the labelled axis. Read each bar's height off the scale, find the tallest bar (the most popular fruit) and the shortest, and try totalling all four. Press Refresh for a brand-new survey.

See it explained