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

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Chapter 4

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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