Take a good look at these reaction-time scores. They are in no order at all, just as they were written down: 7, 5, 8, 6, 7, 9, 6, 8, 7, 5, 9, 6, 7, 8, 6, 7, 5, 8, 7, 9, 6, 7, 8, 6.

Here are three frequency tables from data we collected. Notice how the messy scores become a tidy count, then how spread-out values are grouped into bands. Look closely at the last table and see if you can spot what has gone wrong.

Here is a fresh set of class data: 18 scores to tally into three equal bands. We will agree on the band edges first, then tally each value into its band and check the totals add back to 18. Pupils take turns at the board and the rest of the class agrees or corrects out loud.

Now you meet three different data sets, and for each one you have to choose the right band width. The sets are in the activity below, and each one is spread out differently:

• Set A runs from 1 to 9.
• Set B runs from 5 to 44.
• Set C runs from 12 to 102, the widest spread of the three.

Today's key ideas

• A frequency table records how often each value or band appears, with tally marks grouped in fives for easy reading.
• When values spread too widely, we group them into equal, non-overlapping class intervals.
• Grouping makes data readable but hides the exact individual values, so the band width matters — aim for a width that gives roughly four to six bands.