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# Location

By Levi Clancy for Student Reader on
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TermOverview

Minimum (Min)

The smallest value.

Maximum (Max)

The largest value.

Population Mean (μ)

Equivalent to (ΣX)/N.

Sample Mean (X)

The sample means will perhaps be greater or less than µ, but the average of all possible X will be µ -- X is an unbiased estimation of µ.

Median

Order the data from smallest to largest. If there is an odd number of data, then the median is simply the middle value (position (n+1)/2); if there is an even number of data, then it is the average of the two middle values (position n/2 and (n/2)+1.

Quartiles (Q1, Q2, Q3)

If the data is ordered from smallest to largest, then as the median has 50% of the data below and it 50% of the data above it, Q1 (the first quartile) has 25% of the data at or below it and Q3 (the third quartile) has 25% of the data at or above it. For an odd n, then Q1 is at the position ( n + 3 ) / 4 and for an even n, then Q1 is at the position ( n + 2 ) / 4 and Q3 is intuitively at that same position from the largest number (this can be computed as n minus the position of Q1).