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Calculating Averages from Grouped Data

Part of Grouped Data · GCSE GCSE Mathematics revision

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 8 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 8

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:

Formula: Estimated Mean = Σ(midpoint × frequency) ÷ Σ(frequency)

Step-by-step calculation:

  1. Find the midpoint of each class
  2. Multiply each midpoint by its frequency
  3. Add all these products
  4. Divide by the total frequency
Example calculation:
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:

  1. Find the position: (n + 1) ÷ 2, where n = total frequency
  2. Use cumulative frequency to locate the median class
  3. Use interpolation within the median class

Keep building this topic

Read this section alongside the surrounding pages in Grouped Data. That gives you the full topic sequence instead of a single isolated revision point.

Grouped Frequency Table ExampleExam Tips for Grouped DataMaking Sense of Large DatasetsKey Facts About Grouped Data

Practice Questions for Grouped Data

A frequency table uses the class intervals shown below. | Speed, s (mph) | Frequency | |---|---| | 0 < s ≤ 20 | 4 | | 20 < s ≤ 40 | 11 | | 40 < s ≤ 60 | 9 | | 60 < s ≤ 80 | 2 | A car travels at exactly 40 mph. Which class interval does this value belong to?

  • A. 20 < s ≤ 40
  • B. 0 < s ≤ 20
  • C. 40 < s ≤ 60
  • D. It could belong to either 20 < s ≤ 40 or 40 < s ≤ 60
1 markfoundation

A teacher groups 30 students' test scores into four class intervals and calculates the estimated mean and estimated median. Explain why both the estimated mean and the estimated median from grouped data are only approximations of the true values. In your answer, refer to the assumptions made.

3 marksstandard

Quick Recall Flashcards

What is grouped data?
Grouped data is when individual data values are organized into classes or intervals. For example, heights might be grouped as 150-160cm, 160-170cm, etc.
What is class width?
Class width is the size of each class interval. For '10 ≤ x < 20', the class width is 20 - 10 = 10. Equal class widths make data easier to analyze.

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Grouped Frequency Table Example

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Exam Tips for Grouped Data