Grade 10 Maths · Statistics

Estimate the mean of grouped data

Estimate the mean of grouped data by multiplying each class midpoint by its frequency, adding, and dividing by the total frequency.

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5. Grade 10 Mathematics - Statistics - Estimated Means of Grouped DataJuniorTukkie at the University of Pretoria

Estimated Means from Grouped Data - Corbettmathscorbettmaths

3. Grade 10 Mathematics - Statistics - Calculating x for Means and MediansJuniorTukkie at the University of Pretoria

Grouped data statistics grade 10 with Thapelo RafapaMastering Mathematics with Thapelo Rafapa

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Question 4.2 · September 2024 · Provincial · 4 marks

At a School Athletics Day, a stopwatch was used to find the time it took a group of athletes to run the 200m event. The results were recorded in a frequency table. Diagram for this question

4.2 Calculate the estimated mean.(4)

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More past paper questions: estimate the mean of grouped data

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3. Question 2.3 · November 2024 · Paper 2 · Provincial · 4 marks
The histogram below shows the distribution of examination scores for learners in Introductory stats.
2.3 Estimate the mean of this data. Show all calculations.(4)
Show the memo (4 ticks)Memo
1. ✓
  Add the frequencies $n = 12 + 18 + 55 + 57 + 43 + 11 + 4 = 200$
  1 mark · Estimate the mean of grouped data
2. ✓
  Sum of midpoint × frequencyMidpoints $35; 45; 55; 65; 75; 85; 95$ | $\sum f \cdot x = 420 + 810 + 3025 + 3705 + 3225 + 935 + 380 = 12500$
  1 mark · Estimate the mean of grouped data
3. ✓
  Substitution $\overset{x}{ˉ} = \frac{\sum f \cdot x}{n} = \frac{12 500}{200}$
  1 mark · Estimate the mean of grouped data
4. ✓
  Answer $\overset{x}{ˉ} = 62, 5$
  1 mark · Estimate the mean of grouped data
4. Question a · Siyavula Grade 10 Mathematics, 10.4 Measures of dispersion, Worked example 13 · 3 marks
The mathematics marks of $100$ grade $10$ learners at a school have been collected. The data are presented in the following table: $Diagram for this question$
a Calculate the mean of this grouped data set.(3)
Show the memo (3 ticks)Memo
1. ✓
  MidpointsAssume all the learners in each interval are at the central value of the interval:
  $10; 25; 35; 45; 55; 65; 75; 90$
  1 mark · Estimate the mean of grouped data
2. ✓
  Sum of frequency times midpoint over totalMean $= \frac{2 ( 10 ) + 5 ( 25 ) + 18 ( 35 ) + 22 ( 45 ) + 18 ( 55 ) + 13 ( 65 ) + 12 ( 75 ) + 10 ( 90 )}{100}$
  1 mark · Estimate the mean of grouped data
3. ✓
  Answer $= 54%$
  1 mark · Estimate the mean of grouped data

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