Grade 11 Maths · Statistics

Calculate and use standard deviation

Find the standard deviation to measure how spread out data is from the mean, for example how many values lie within one standard deviation.

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

4. Grade 11 Mathematics - Statistics - Standard Deviation CalculationsJuniorTukkie at the University of Pretoria

Statistics Grade 11 | How to Calculate Standard Deviation ( Using Calcutor)Gridwell Maths Tutoring

How many scores are within one standard deviations from the mean grade 11 and grade 12 statisticsBenit mathematics

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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)

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More past paper questions: calculate and use standard deviation

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3. Question 1.3 · November 2024 · Paper 2 · Provincial · 2 marks
The traffic department set up a roadblock on the N12 between Potchefstroom and Klerksdorp. During the first hour, they stopped 11 minibus taxis.
The following dataset is a summary of the number of passengers per minibus taxi.

18, 26, 25, 18, 16, 12, 10, 8, 18, 17, 8
1.3 Taxis in which the number of passengers is more than one standard deviation above the average can be considered overloaded.
How many taxis were overloaded?(2)
Show the memo (2 ticks)Memo
1. ✓
  IntervalInterval $= 16 + 5, 83$
  $= 21, 83$
  1 mark · Calculate and use standard deviation
2. ✓
  Answer $∴$ 2 of the taxis are overloaded.
  1 mark · Calculate and use standard deviation
4. 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
5. 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
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

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