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15 Cards in this Set

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variation
Variation reflected in a data set is the difference among the data values.
range
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)
mean absolute deviation
a more efficient measure of dispersion that utilizes all data values
deviation
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
n
sample size
absolute deviation
The absolute values of the deviations, naturally called absolute deviations, are the unsigned distances from the data values to the sample mean.
Σ
sum
mean absolute deviation (MAD)
the sum of all the absolute deviations / the number of data values
s
the sample standard deviation
sample standard deviation
square root of:
the sum of the squares of the deviation / n-1
shortcut formula for standard deviation
square root of:
n(the sum of the squares of the data values)-(the sum of the data values)squared / n(n-1)
The Empirical Rule
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.
μ
population mean

the sum of all the observations in the population / N

N= the number of elements in a population
σ
population standard deviation
position of the kth percentile
(n+1)k / 100