Statistics

Mean, median and mode of grouped data (class intervals with frequencies).

Key ideas

• For grouped data, use the class mark (the middle of each class) as the value of the class.
• The mean can be found directly, by the assumed-mean method, or by step deviation; all give the same answer.
• The modal class is the class with the highest frequency.
• The median class is the class whose cumulative frequency first reaches n/2 or more.
• In the median formula, cf is the cumulative frequency of the class just before the median class.
• h is the class width; l is the lower limit of the modal or median class.

Remember

Watch out

• Using the class limits instead of the class mark for the mean.
• Taking cf of the median class itself instead of the class before it.
• Choosing the class with the largest values as the modal class (it is the largest frequency).

Worked example