Mean of grouped data
A class's test marks are grouped 0–10, 10–20, …, 40–50. Change how many students scored 20–30 and 40–50, and find the mean from the class marks, directly and with an assumed mean.
Core concept
For grouped data each class is represented by its class mark x (the middle of the class); the mean is Σfx ÷ Σf, or A + Σfd ÷ Σf with an assumed mean A and d = x − A, and both ways give the same answer
Topic: Statistics
When marks are grouped into classes we no longer know each mark, so each class is stood for by its class mark, the middle value: 5 for 0–10, 15 for 10–20, and so on. Multiply each class mark x by its frequency f, add the products and divide by the number of students: mean = Σfx ÷ Σf. A quicker way picks an assumed mean A near the middle, here 25, finds each deviation d = x − A and uses mean = A + Σfd ÷ Σf. The numbers fd are small and easy to add, and the answer is the same.
What you will learn
- Find the class mark of each class.
- Calculate the mean of grouped data as Σfx ÷ Σf.
- Use an assumed mean and deviations to find the same mean.
- Explain how changing a frequency moves the mean.
Before you start
- Know the mean of ungrouped data and how to read a frequency table.
Materials
- The marks of your class in a test, grouped into classes of 10
Equipment
- A calculator
Procedure
- Record the table with 12 students in 20–30 and 5 in 40–50.
- Change 40–50 to 15 students and record.
- Change 20–30 to 4 students and record.
- Compare the two ways of finding the mean each time.
How this simulation is simplified
- Every mark in a class is taken to be its class mark; the other frequencies are 5, 8 and 10.