Measures of Location and Spread

Measure of Location

A single value which describes a position in a data set

Measure of central tendency

The single value which describes the centre of the data

Mode/Modal Class

Value or class that occurs most often

Median

Middle value when the data values are put in order

Mean

xbar = (Σx)/n or for grouped data xbar = (Σxf)/Σf

Lower Quartile

¼ of the way through the set (median of lower half)

Upper Quartile

¾ of the way through the set (median of upper half)

Percentile

Data is split into 100 parts

How to find Q1 for discrete data

Divide n by 4
If a whole number, Q1 is halfway between this data point and the one above
If not a whole number, round up and pick this data point as Q1

How to find Q3 for discrete data

Find ¾ of n
If a whole number, Q3 is halfway between this data point and the one above
If not a whole number, round up and pick this data point to be Q3

How to find quartiles for grouped frequency tables

Use interpolation (by assuming that the data values are evenly distributed within each class)
Q1 = n/4th data value
Q2 = n/2th data value
Q3 = 3n/4th data value

Range

The difference between the largest and smallest values in the data set

IQR

The difference between Q1 and Q3 (Q3-Q1)

Interpercentile range

The difference between the values for 2 given percentiles

Variance

A statistical measure of how far a set of numbers are spread out from the mean

Variance equation

Standard Deviation

The square root of variance

Variance equation for a grouped frequency table

Coding

A way of simplifying statistical calculations

Formula for Coding

y = (x-a) / b