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15 Cards in this Set
- Front
- Back
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variation
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Variation reflected in a data set is the difference among the data values.
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range
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The distance between the largest and smallest data values is called the range of a data set:
Range = the largest value (maximum) - the smallest value (minimum) |
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mean absolute deviation
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a more efficient measure of dispersion that utilizes all data values
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deviation
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The difference between a data value and the sample mean is called the deviation of that data value:
Deviation of a data value = the data value - the sample mean |
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n
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sample size
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absolute deviation
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The absolute values of the deviations, naturally called absolute deviations, are the unsigned distances from the data values to the sample mean.
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Σ
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sum
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mean absolute deviation (MAD)
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the sum of all the absolute deviations / the number of data values
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s
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the sample standard deviation
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sample standard deviation
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square root of:
the sum of the squares of the deviation / n-1 |
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shortcut formula for standard deviation
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square root of:
n(the sum of the squares of the data values)-(the sum of the data values)squared / n(n-1) |
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The Empirical Rule
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If the distribution of the data is bell-shaped, then
1. Approximately 68% of the observations will be within one standard deviation of the mean. 2. Approximately 95% of the observations will be within two standard deviations of the mean. 3. Approximately 99.7% of the observations will be within three standard deviations of the mean. |
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μ
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population mean
the sum of all the observations in the population / N N= the number of elements in a population |
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σ
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population standard deviation
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position of the kth percentile
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(n+1)k / 100
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