Mathematics

Mathematics

Problem

The table shows information about the time, in minutes, spent on homework by each of 32 pupils in one night.
Time (tt minutes)Number of pupils
0<t≤200 < t \leq 207
20<t≤4020 < t \leq 4016
40<t≤6040 < t \leq 603
60<t≤8060 < t \leq 806
Estimate the mean time spent on homework.
Intuitive explanation

To find the mean from grouped data, you need to find the midpoint of each class interval—that's your best estimate for where all the data in that group actually sits. Then multiply each midpoint by how many pupils fall into that group, add them all up, and divide by the total number of pupils. The key is treating each interval as if all its pupils spent time equal to the middle value.

Intuitive explanation

To find the mean from grouped data, you need to find the midpoint of each class interval—that's your best estimate for where all the data in that group actually sits. Then multiply each midpoint by how many pupils fall into that group, add them all up, and divide by the total number of pupils. The key is treating each interval as if all its pupils spent time equal to the middle value.

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