Grouping numbers into intervals — Data, 7–10
When there are many measurements, putting nearby numbers together can make the pattern easier to see. The groups must be chosen carefully so that the picture does not hide important differences.
Numbers can live in groups
Imagine recording the heights of every child in a large school. Instead of writing every height separately, you could count how many are 120–129 cm, 130–139 cm, and so on. These are intervals: groups of nearby values that give a quick picture of the whole set.
Why make groups?
A long list is hard to scan, especially when it contains hundreds of values. Groups turn a crowded list into a shape you can compare: perhaps most children are in the middle, with only a few at either end. The cost is that you lose exact details inside each group.
Grouping jump distances
Four jumps measure 121, 127, 134 and 146 cm. Use intervals of ten: 120–129 contains 121 and 127, so it has 2 jumps; 130–139 contains 134, so it has 1; 140–149 contains 146, so it has 1. The groups show that the first interval is the busiest.
The boundary trap
A common mistake is putting 130 into both 120–130 and 130–140, or into neither. That feels reasonable because the endpoint touches both labels. Decide on one clear rule, such as 120–129 and 130–139, and use it for every value. Consistent boundaries keep the count correct.
Where groups help
Weather reports group temperatures so we can see whether a week was mostly cool or warm. Shops group customers by ages or spending ranges, and sports clubs group times or distances when many people take part. In each case, the groups make a large collection easier to describe, but they do not replace the original measurements.
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