Here is a messy list of reaction-time scores, just numbers scattered across the board with no order at all: 7, 5, 8, 6, 7, 9, 6, 8, 7, 5, 9, 6, 7, 8, 6, 7, 5, 8, 7, 9, 6, 7, 8, 6. Take a good look at them.

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.

Today we explore: here is a fresh set of class data — 18 scores to tally into three equal bands: 4, 11, 20, 7, 15, 22, 9, 13, 25, 6, 18, 21, 8, 14, 27, 12, 19, 24. We will agree on the band edges first, then tally each value into its band and check the totals add back to 18.

Today we work through three different data sets, and we have to choose the right band width for each one. Here are the sets on the board:

• Set A: 2, 5, 8, 3, 7, 9, 4, 6, 1, 8, 5, 3 (values run 1 to 9)
• Set B: 12, 27, 35, 8, 19, 41, 23, 16, 38, 29, 5, 44 (values run 5 to 44)
• Set C: 65, 23, 91, 48, 12, 77, 34, 88, 56, 19, 102, 71 (values run 12 to 102)

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.