This deep dive covers Calculating Averages from Grouped Data within Grouped Data for GCSE Mathematics. Revise Grouped Data in Statistics for GCSE Mathematics with 14 exam-style questions and 20 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 4 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 4 of 7
Practice
14 questions
Recall
20 flashcards
Calculating Averages from Grouped Data
1. Modal Class
The modal class is simply the class interval with the highest frequency. In our example above, it's 170 ≤ h < 180 with frequency 15.
2. Estimated Mean
Since we don't know the exact values, we use the midpoint of each class to estimate the mean:
Step-by-step calculation:
- Find the midpoint of each class
- Multiply each midpoint by its frequency
- Add all these products
- Divide by the total frequency
Σ(fx) = (155×5) + (165×12) + (175×15) + (185×8) + (195×3)
= 775 + 1980 + 2625 + 1480 + 585 = 7445
Total frequency = 5 + 12 + 15 + 8 + 3 = 43
Estimated mean = 7445 ÷ 43 = 173.1 cm
3. Estimated Median
To find which class contains the median:
- Find the position: (n + 1) ÷ 2, where n = total frequency
- Use cumulative frequency to locate the median class
- Use interpolation within the median class