psychology 2910 - lecture 5 (variability)

Variability

A quantitative measure of the degree to which scores in a distribution are spread out or clustered together

Consists of: range (interquartile range), standard deviation, and variance

Range

The difference between the high score and low score; indicates some additional info about scores; influenced by extreme scores

- Small: closer to mean

- Large: farther away from mean

How do you calculate range?

Range = Max - Min

Range = 22 - 9 = 13

Interquartile Range

Range covered by middle 50%; covered with percentiles

Q3 = 75th percentile

Q2 = 50th percentile or median

Q1 = 25th percentile

Interquartile Range: Q3 - Q1

Standard Deviation

Describes the "average" or "typical" or "representative" distance from the mean; most widely used measure of variability

- If the standard deviation were 15.00, the scores would be more spread out than if the standard deviation were 10.00

How are sample statistics estimates of population parameters?

Standard deviation of a sample = estimate of standard deviation of population

Mean of a sample = estimate of mean of a population

What is an analogy to better understand degrees of freedom (n - 1)?

12 parking spots:

- First person: free to park in any spot

- Second person: free to park in any remaining spot

- 11th person: free to park in either of two remaining spots

- 12th person: has no choice; only one spot left

Therefore, there are 11 degrees of freedom (because the numbers must produce the mean)

What percentage of scores are between ± 1 standard deviation of the mean?

Approx. 66%; 68% is more accurate, but 2/3 is close enough

What percentage of scores are between ± 2 standard deviations of the mean?

Approx. 95%

What percentage of scores are between ± 3 standard deviations of the mean?

Approx. 99%