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The Range

The difference between the highest and lowest values in a data set

The Quartiles

Split the data into 4, equally sized sections

The lower quartile

25% of the observations have a value less than Q1

The lower quartile in discrete data

n/4; if a whole number find the midpoint of the corresponding term and the term above; if a decimal, round up and pick the corresponding term

The lower quartile in continuous data

n/4; use interpolation to find the value of the corresponding term

The upper quartile

25% of the observations have a value greater than Q3

The upper quartile in discrete data

3n/4; if a whole number find the midpoint of the corresponding term and the term above; if a decimal, round up and pick the corresponding term

The upper quartile in continuous data

3n/4; use interpolation to find the value of the corresponding term

The inter quartile range

Q3-Q1

Percentiles

Split the data into 100 parts

To calculate the xth percentile

Px = xn/100

The n% to m% interpercentile range

Pm - Pn

The deviation

The difference between the observation made and the mean of the data set

The variance

The mean of the square minus the square of the mean

The standard deviation

The square root of the variance

Lower case sigma, σ

Standard deviation of the data set

Variance and standard deviation in grouped data

Uses the midpoint of groups and multiplies by the frequency. In other words the variance becomes: the sum of the frequency of each class multiplied by the square of the class' midpoint, divided by the sum of the frequency, minus the sum of the frequency of each class multiplied by the class' midpoint, divided by the sum of the frequency, all squared

Adding and subtracting numbers when coding

Does not change the standard deviation of the data

Multiplying and dividing when coding

Does affect the standard deviation of the data

To find the standard deviation using coded data

Find the standard deviation of the coded data and reverse any multiplication or division process applied in the coding