Variability
Definition and Context:

Quantitative measure of the spread (or clustering) of our data

In relation to central tendency  can tell us how much variation there is around a measure of CT

Range, IQR, std deviation/variance
Measures of Variability
1) Range:
Distance between the highest and lowest scores = highest score – lowest score
Example:
58, 73, 74, 76, 78, 81, 90, 96
Range = 9658 = 38
More to note about the Range
1.
Crude and unreliable
–
Distribution 1
: 1, 20,
40,
60,
100
Range= 100 – 1= 99
–
Distribution 2
: 1, 2,
2,
4,
100
Range= 100 – 1= 99
–
Distribution 3
: 1, 98,
99,
100,
100
Range= 100 – 1= 99
2) Interquartile range
(IQR):
First quartile
Q1
the score that separates the lowest 25% of the distribution from the rest
Second quartile
Q2
score that separates the distribution into two half or 50% (median)
Third quartile
Q3
score that separates the bottom 75% of the distribution from the top quarter
**IQR is the distance between the 1
st
and 3
rd
quartile:
IQR = Q3 – Q1
Example: 58, 73, 74, 76, 78, 81, 90, 96
Q2 = median = 77
Q1 = 73.5, Q3 = 85.5
IQR = 85.573.5 = 12
More to note about IQR: