Why grouped data only gives an estimate
Once data is grouped, the exact values are lost — so the mean can only be estimated.
Last year you found a mean straight from a frequency table, where every value was written down exactly. This year the data is grouped — sorted into class intervals like — and that changes everything.
Inside a group such as "8 students between 150 and 160 cm" you no longer know the exact heights. They could all be 151 cm, or spread evenly, or anything in between. The exact total height is genuinely unknown.
Because the exact values are gone, you cannot find an exact mean. The best you can do is a sensible estimate — and the clever trick for that is to use the midpoint of each class. That is the heart of this year's work, and the next section shows you how.
- Grouped data sorts values into class intervals.
- Inside a class interval the exact values are unknown.
- An exact mean is therefore impossible to find.
- Instead you calculate a sensible estimated mean.