Sheet № 182 · Foundation + Higher · AQA · Edexcel · OCR
Estimated Mean from Grouped Data –
Calculating the estimated mean from grouped data is one of the most frequently tested statistics skills on AQA, Edexcel and OCR GCSE papers at both Foundation and Higher level. Because grouped data does not show individual values, you must use the midpoint of each class to estimate the mean. This guide explains the full method, shows you
§Key definitions
Question:
The table shows the masses of 20 parcels.
Answer:
The estimated mean mass is 3.9 kg.
(a)
Midpoints: 5, 15, 25, 40.
(b)
The class with the highest frequency is 20 < h ≤ 30 (frequency 18). Modal class = 20 < h ≤ 30.
(c)
The mean is an estimate because we do not know the exact heights of the plants — we use the midpoint of each class as a representative value, but the actual values may differ.
§Formulas to memorise
Midpoint = (Lower bound + Upper bound) ÷ 2
Estimated mean = Σfx ÷ Σf
Divide: Estimated mean = Σfx ÷ Σf.
Estimated mean = 78 ÷ 20 = 3.9 kg.
Estimated mean = 1075 ÷ 50 = 21.5 cm.
Worked example
The table shows the masses of 20 parcels. | Mass (kg) | 0 < m ≤ 2 | 2 < m ≤ 4 | 4 < m ≤ 6 | 6 < m ≤ 8 | |---|---|---|---|---| | Frequency | 3 | 8 | 6 | 3 | Calculate the estimated mean mass.
Working:
⚠ Common mistakes
- ✗Using class boundaries instead of midpoints. Always calculate (lower + upper) ÷ 2 for each class.
- ✗Forgetting to multiply frequency by midpoint. Each row needs fx, not just x.
- ✗Saying the answer is exact. Always state that the result is an estimated mean because the data is grouped.
✦ Exam tips
- →Set out your working in a table with columns for class, frequency, midpoint and fx — this makes the method clear and earns method marks.
- →The modal class is the class with the highest frequency — it is often asked as a quick-fire part of the same question.
- →If class widths are unequal, be extra careful with midpoints — they must still be calculated individually.
- →For raw data means, see finding the mean. For key formulas, visit our GCSE Maths formulas page.