Mean of grouped data and cumulative frequency
Estimate the mean of grouped data with a midpoint × frequency column, combine two classes' averages properly, build a cumulative frequency column and graph, and read the median off the graph.
- UK: Year 10
- France: grade 8
- Iran: grade 8
- Afghanistan: grade 8
- Syria: grade 8
- Palestine: grade 9
Guide
This studio follows GCSE Statistics: estimating the mean from a grouped frequency table, and cumulative frequency graphs.
When data is grouped we no longer have the single values, so we estimate the mean: we pretend every value in a class sits at the class midpoint. Multiply each midpoint by its frequency, add these products, and divide by the total frequency, not by the number of classes.
Combining the averages of two groups of different sizes works the same way: the bigger group counts for more (a weighted mean).
The cumulative frequency of a class is the number of values in it and in all the classes before it: a running total. Its points are plotted at the upper end of each class, because only there have all of that class's values been counted. The median is where the graph reaches half the total frequency.
Ask: "Why is the mean from a grouped table only an estimate?"