Sheet № 119 · Foundation + Higher · AQA · Edexcel · OCR
Mean from a Frequency Table –
Calculating the mean from a frequency table is one of the most common statistics questions on both Foundation and Higher GCSE papers. Whether the data is ungrouped or grouped, the core method is the same: multiply each value (or midpoint) by its frequency, add them up, and divide by the total frequency. This guide covers both types, along
§Key definitions
Question:
The table shows the number of pets owned by 30 students. Find the mean.
Answer:
The mean number of pets is 1.73.
Q1 (Foundation):
Find the mean from this frequency table.
Q2 (Foundation):
The modal value in Q1 is the value with the highest frequency. State the mode.
Q3 (Higher):
Heights of 40 plants are recorded below. Calculate the estimated mean.
§Formulas to memorise
Mean = Σfx ÷ Σf
Midpoint = (Lower bound + Upper bound) ÷ 2
If grouped — , find the midpoint of each class interval.
Multiply — each value (or midpoint) by its frequency to create the fx column.
Add up — all the fx values to get Σfx.
Add up — all the frequencies to get Σf.
Divide — Σfx by Σf to get the mean.
Worked example
The table shows the number of pets owned by 30 students. Find the mean. | Pets | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | Frequency | 5 | 8 | 10 | 4 | 3 |
Working: fx values: 0×5=0, 1×8=8, 2×10=20, 3×4=12, 4×3=12. Σfx = 0 + 8 + 20 + 12 + 12 = 52. Σf = 5 + 8 + 10 + 4 + 3 = 30. Mean = 52 ÷ 30 = 1.73 (to 3 s.f.).
⚠ Common mistakes
- ✗Using class boundaries instead of midpoints. For grouped data, always calculate the midpoint of each class. Do not use the lower or upper boundary.
- ✗Dividing by the number of classes instead of the total frequency. The denominator is Σf (total number of data items), not the number of rows in the table.
- ✗Forgetting the last class has a different width. In the worked example above, 80-100 has a midpoint of 90 (not 89.5) because the class includes 100. Read class boundaries carefully.
✦ Exam tips
- →Add extra columns to the table for midpoints and fx — examiners expect to see this working and award marks for it.
- →For the class containing the median, use cumulative frequency. The median position is at the (n + 1)/2 th value (or n/2 th for grouped data).
- →Always label your answer "estimated mean" when working with grouped data to show you understand it is an approximation.