Chapter 3: Measures of Variability

Question 1

Range

Answer 1

Largest value minus the smallest value

Con: swayed by outliers

Question 2

Interquartile Range

Answer 2

The range of the middle 50% of the data

Pro: less influenced by extreme values

Question 3

Five Number Summary

Answer 3

1. Smallest value (within the inner fences)
2. Q1
3. Q2
4. Q3
5. Largest Value (within the inner fences)

Used to create box and whisker plots

Question 4

Outlier Identification

Answer 4

Mild: any observation that falls above or below the mild fences (represented by a circle or dot)

Extreme: any observation that falls above or below the extreme fences (represented by an asterisk)

See formula sheet

Question 5

Deviation Score

Answer 5

the difference between an observation and the mean

These scores MUST be squared to compute variance because they add up to zero

Question 6

Total Variability

Answer 6

sum of squares

Question 7

Variance

Answer 7

The average squared distance from the mean

Question 8

Degrees of Freedom

Answer 8

(n-1)

The denominator for the sample variance formula → makes the sample variance an unbiased estimator

Question 9

Standard Deviation

Answer 9

The average distance from the mean

Question 10

Coefficient of Variability

Answer 10

average relative distance from the mean

Question 11

Empirical Rule

Answer 11

FOR NORMAL DATA ONLY

identifies the percent of data that fall within a specified number of standard deviations from the mean

Question 12

Chebychev’s Theorem

Answer 12

FOR ALL TYPES OF DATA

identifies the MINIMUM percentage of data that fall within a specified number of standard deviations from the mean