# PY 211 Lecture Notes - Lecture 7: Interquartile Range, Standard Deviation, Variance

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Variability
Measuring Variability
A. Definition
Variability is the dispersion (spread) of data in a distribution
B. Measures of Variability
1. Range
2. Interquartile range
-Semi interquartile range
3. Variance
- Standard deviation
The Range
A. Definition
The difference between the largest value (L) and smallest value (s) in a set of data
Range = largest smallest
B. Characteristics
1. Only considers the largest and smallest values in distribution
2. Simplest way to describe the dispersion of scores
3. Informative for data without “outliers”
C. Examples
1. Scores: 5, 14, 7, 21, 13, 8
Range = 21 5 = 16 (more dispersed)
2. Scores: 5, 6, 7, 7, 4, 8
Range = 8 4 = 4
3. Scores: 5, 7, 8, 20, 19, 21
Range = 21 5 = 16
What is the range for the following list of scores? 1, 3, 2, 5, 7, 2
Range = 7 1 = 6
The Variance
A. Definition
1. The average squared distance that scores deviate from their mean
2. On average, how far do scores deviate from the mean?
B. Population Variance Definitional Formula
1. Deviation
a. How far a score is from the mean
b. Deviation = x - (population)
c. Deviation = x M (sample)
2. Average Deviation
average deviation = (x-) / N
N = number of data points
Example 1
2, 3, 4, 5, 6
x = 2 + 3+4+5+6 = 20
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