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Term 2 · Week 2 · Data and Descriptive Statistics

Challenge problem

Challenge

Daily maximum temperatures for a week (°C): 30, 32, 34, 31, 33. Find the population standard deviation to two decimal places.

Show step-by-step solution

Answer: 1.41 °C

  1. Mean =(30+32+34+31+33)/5=32= (30+32+34+31+33)/5 = 32.
  2. Squared deviations: 4,0,4,1,14, 0, 4, 1, 1; sum =10= 10.
  3. Variance =10/5=2= 10/5 = 2; standard deviation =2≈1.41°C= \sqrt{2} \approx 1.41°\text{C}.

Common errors to watch for

  • Dividing by n−1=4n-1=4 gives the sample SD 1.58; the item asks for the population SD.

Budget of Work competencies

  • gm11.t2.w2.c3
    Identify the appropriate measure of central tendency and measures of variability of a given data set for different purposes.
  • gm11.t2.w2.c4
    Use appropriate technologies (e.g., calculator, Excel, Jamovi, Geogebra, etc.) to calculate measures of central tendency and variability.

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