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Level 3

Representation And Summary Of Data - Dispersion


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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