Worksheet 13: Variability

Worksheet 13: Variability#

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  1. Think of examples of scenarios where you care not only where the data is centered, but also what the variability is.

  2. Come up with a suggestion for one or more quantitative measures of variability.

Variance and Standard Deviation.

  1. The list of rowers’ heights (in inches) is \((71,72,60,73,71,72,72,73,71)\). Calculate the variance of the rowers’ heights. What are the units of the variance?

  2. Calculate the standard deviation of the rowers’ heights.

  3. Suppose someone offers you a choice between: (1) A gift of $100 (2) The chance to flip a fair coin for $300. Calculate the mean and standard deviation of your earnings in each scenario.

  4. Reflecting about standard deviation:

    a. Do you think the standard deviation is a satisfying measure of variability? What is it conveying? What is it not conveying?

    b. Suppose you know the mean and standard deviation. Can you infer that a “typical” sample is within 1 standard deviation of the mean?

Quantiles

  1. How can we use quantiles to measure variability?

  2. How does the information we get from the standard deviation differ from the information we get from the quantiles?

  3. 80% of data points in the histogram fall between the 10th and 90th percentile. Why?