Grade 11 Maths · Statistics · Paper 2

Variance and Standard Deviation Grade 11

Real Variance and Standard Deviation past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 10 past paper questions
skill: 1 skill
videos: 1 videos

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Question 1.3 · May/June 2025 · Paper 2 · National (DBE) · 2 marks

An insurance broker signed contracts with 15 people. The monthly premium (in rands) payable on each contract is given below.

134, 215, 325, 326, 362, 429, 515, 531, 598, 610, 624, 728, 923, 1034, 1200

1.3 Calculate how many monthly premiums are within ONE standard deviation of the mean.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Variance and Standard Deviation skills

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Calculate and use standard deviationFind the standard deviation to measure how spread out data is from the mean, for example how many values lie within one standard deviation.11 past paper questions · 4 videos

More Variance and Standard Deviation Grade 11 questions and answers

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4. Question WE11 · Siyavula Grade 11 Mathematics, 11.4 Variance and standard deviation, Worked example 11 · 3 marks
WE11 What is the variance and standard deviation of the possibilities associated with rolling a fair die?(3)
Show the memo (3 ticks)Memo
1. ✓
  MeanThe data set is $x = {1; 2; 3; 4; 5; 6}$ and $n = 6$ .
  $\overline{x} = \frac{1}{6} (1 + 2 + 3 + 4 + 5 + 6) = 3, 5$
  1 mark · Calculate the mean
2. ✓
  Variance $σ^{2} = \frac{\sum ( x - x ) ^{2}}{n} = \frac{1}{6} (6, 25 + 2, 25 + 0, 25 + 0, 25 + 2, 25 + 6, 25) = 2, 917$
  1 mark · Calculate and use standard deviation
3. ✓
  Standard deviation $σ = 2, 917 = 1, 708$
  1 mark · Calculate and use standard deviation
5. Question b · Siyavula Grade 12 Mathematics, 9.1 Revision, Worked example 2 · 2 marks
You flip a coin $100$ times and it lands on heads $44$ times. You then use the same coin and do another $100$ flips. This time it lands on heads $49$ times. You repeat this experiment a total of $10$ times and get the following results for the number of heads.
${44; 49; 52; 62; 53; 48; 54; 49; 46; 51}$
For the data set above:
b Calculate the variance and standard deviation using a table.(2)
Show the memo (2 ticks)Memo
1. ✓
  Squared deviations $x_{i} - \overline{x}$ : $- 6, 8$ ; $- 1, 8$ ; $1, 2$ ; $11, 2$ ; $2, 2$ ; $- 2, 8$ ; $3, 2$ ; $- 1, 8$ ; $- 4, 8$ ; $0, 2$
  $(x_{i} - \overline{x})^{2}$ : $46, 24$ ; $3, 24$ ; $1, 44$ ; $125, 44$ ; $4, 84$ ; $7, 84$ ; $10, 24$ ; $3, 24$ ; $23, 04$ ; $0, 04$
  1 mark · Calculate and use standard deviation
2. ✓
  Variance $σ^{2} = \frac{\sum ( x _{i} - x ) ^{2}}{n} = \frac{225 , 6}{10} = 22, 56$
  1 mark · Calculate and use standard deviation
6. Question d · Siyavula Grade 12 Mathematics, 9.3 Correlation, Worked example 9 · 3 marks
A cardiologist wanted to test the relationship between resting heart rate and the peak heart rate during exercise. Heart rate is measured in beats per minute (bpm). The following set of data was generated from $12$ study participants after they had run on a treadmill at $10 km/h$ for $10$ minutes. $Diagram for this question$
d Without using your calculator, find the correlation coefficient, $r$ . Confirm your answer using your calculator.(3)
Show the memo (3 ticks)Memo
1. ✓
  Standard deviation of x $r = b \frac{σ _{x}}{σ _{y}}$
  $\overset{x}{ˉ} = \frac{852}{12} = 71$ ; $\sum (x_{i} - \overset{x}{ˉ})^{2} = 1534$
  $σ_{x} = \frac{1 534}{12} = 11, 31$
  1 mark · Calculate and use standard deviation
2. ✓
  Standard deviation of y $\overset{y}{ˉ} = \frac{1 858}{12} = 154, 83$ ; $\sum (y_{i} - \overset{y}{ˉ})^{2} = 1861, 68$
  $σ_{y} = \frac{1 861 , 68}{12} = 12, 46$
  1 mark · Calculate and use standard deviation
3. ✓
  r $r = 0, 96 \times \frac{11 , 31}{12 , 46} = 0, 87$
  On the calculator (statistics mode, recall $r$ ): $r = 0, 87$
  1 mark · Find and describe the correlation

Variance and Standard Deviation Grade 11 videos

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3. Grade 11 Mathematics - Statistics - Standard DeviationJuniorTukkie at the University of Pretoria

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