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15 Cards in this Set
 Front
 Back
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 / n1 

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(n1) 

The Empirical Rule

If the distribution of the data is bellshaped, 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
