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Probability and Statistics: Descriptive statistics · Measures of Central Tendency

How the mean, median and mode summarize data, how outliers and skew pull them apart, and which one to trust in a given situation.

Probability and Statistics · 24 questions

Try 3 questions

1. The arithmetic mean is often called the "balance point" of the data. What property justifies that name?

  1. Half the values always lie on each side
  2. It is always one of the observed values
  3. Deviations from it always sum to zero
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Answer: Deviations from it always sum to zero

Distances above the mean exactly cancel distances below it, like weights balancing on a seesaw. Having half the values on each side is the median's property.

2. Five houses sit along a straight road. Where should a shared mailbox go to minimize the total walking distance for all households?

  1. At the position of the middle house
  2. Halfway between the two end houses
  3. At the mean position of the houses
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Answer: At the position of the middle house

The median minimizes the sum of absolute distances; the mean instead minimizes the sum of squared distances, which overweights far-off houses.

3. Household incomes in most countries are strongly right-skewed. Which measure best describes a typical household's income?

  1. The midrange of lowest and highest income
  2. The mean, because it uses every value
  3. The median, because extremes barely affect it
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Answer: The median, because extremes barely affect it

A small number of very high incomes pulls the mean upward, while the median stays where the middle household actually is.

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