The spread of a series
Range, interquartile range, variance, standard deviation, coefficient of variation, box plot, outliers, and the effect of a shift or a change of unit.
- 27 cards
- 5 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
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A few cards from the deck
Range: what is it?
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The difference between the largest and the smallest value of the series.
It is the simplest measure, but it only looks at two values: a single outlier is enough to blow it up.
What is the standard deviation of the series 2, 4, 6, 8, 10 (variance computed with divisor n)?
- 2.83
- 8
- 3.16
- 2.4
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2.83
The mean is 6, the deviations −4, −2, 0, 2, 4 have squares 16, 4, 0, 4, 16: variance 40 / 5 = 8, standard deviation √8 ≈ 2.83. 8 forgets the root, 3.16 divides by n − 1, 2.4 is the mean absolute deviation.
The variance is the mean of the … of the deviations from the …; the deviations themselves are not averaged, because their sum is zero.
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The variance is the mean of the squares of the deviations from the mean; the deviations themselves are not averaged, because their sum is zero.
Positive and negative deviations cancel out exactly. Squares are never negative: the more the series spreads, the larger the mean of the squares.
Interquartile range: what is it?
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The difference between the third and the first quartile: the width of the interval holding the central half of the series.
Extreme values barely affect it, unlike the range or the standard deviation: it naturally goes with the median.