# PSYC 2300 Lecture Notes - Lecture 11: Squared Deviations From The Mean, Standard Deviation

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Variability

1. Overview

a. Variability can be defined in several ways

i. Numerical difference between scores (quantitative distance)

ii. Distance of a score from mean

b. Purposes of variability

i. Describe distribution

ii. Measures how well an individual score represents distribution

c. 3 measures

i. Range

ii. Standard deviation

iii. Variance

2. Range

a. Smallest to largest

b. Difference between maximum and minimum

c. If using continuous data

i.

d. Crude and unreliable measure

i. Not resistant to extremes

ii. Based on 2 scores, not all data

e. IQE is measure of range/difference between upper & lower quartiles

3. Standard deviation and variance

a. Standard deviation—most common and most important

b. Standard distance from mean

c. Tells us if the scores are clustered around mean or widely scattered

d. Variance is a companion measure

e. Calculating standard deviation and variance

i. Determine deviation (distances from mean)

1. Deviation score:

a. Do this for each score

ii. Calculate average deviation

iii. Get rid of +/- in deviations

1. Square each deviation

2. Sum squared deviations

a. Variance

3. Average squared deviations

iv. Find standard deviation

1.

2.

f. SS: sum of squared deviations

i. So…variance=SS/n

ii. 2 ways to compute

1. —definitional formula