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Term 2 · Week 2 · Data and Descriptive Statistics

Challenge problem

Challenge

Find the population standard deviation of 2,4,4,4,5,5,7,92, 4, 4, 4, 5, 5, 7, 9.

Show step-by-step solution

Answer: 2

  1. Mean: 40÷8=540 \div 8 = 5.
  2. Squared deviations: 9,1,1,1,0,0,4,169, 1, 1, 1, 0, 0, 4, 16; sum =32= 32.
  3. Variance =32÷8=4= 32 \div 8 = 4, so σ=4=2\sigma = \sqrt{4} = 2.

Common errors to watch for

  • Forgetting to take the square root reports the variance (4).
  • Dividing by n−1=7n - 1 = 7 gives the sample SD ≈ 2.14.

Budget of Work competencies

  • gm11.t2.w2.c4
    Use appropriate technologies (e.g., calculator, Excel, Jamovi, Geogebra, etc.) to calculate measures of central tendency and variability.
  • gm11.t2.w2.c5
    Interpret the computed measures of central tendency and variability.

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