GRAVETTER_CH04_INTRODUCTION OF VARIABILITY

Question 1

What is the statistical term that provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together?

Answer 1

Variability

Question 2

THINK! What is the purpose for measuring variability?

Answer 2

To obtain an objective measure of how the scores are spread out in a distribution.

Question 3

TRUE OR FALSE: Variability describes whether the scores in a distribution are clustered close together, or are spread out over a large distance.

Answer 3

TRUE.

Question 4

TRUE OR FALSE: Variability measures how well an individual score (or group of scores) represents the entire distribution.

Answer 4

TRUE.

In this vase, variability provides information about how much error to expect if you are using a sample to represent a population.

Question 5

THINK! What are three different measures of variability?

Answer 5

1. Range
2. Standard deviation
3. Variance

Question 6

Which measure of variability is the distance covered by the scores in a distribution, from the smallest score to the largest score?

Answer 6

Range

X(max)-X(min) or largest score minus smallest score

Question 7

THINK! What is the range of a distribution of scores (with precisely defined upper and lower boundaries—does this mean discrete variables?) having values from 1 to 5

Answer 7

4 points.

Question 8

THINK! What is the difference between the algebraic definitions of range between a continuous variable and a discrete variable?

Answer 8

Measurements of discrete variables
range = Xmax - Xmin
ex. Scores having values from 1 to 5 cover a range of 4 points

Measurements of continuous variables
range = URL for Xmax - LRL for Xmin
ex. Scores having values from 1 to 5 (LRL 0.5 and URL 5.5) cover a range of 5 points

Question 9

THINK! When the scores are all whole numbers (e.g. a variable like number of children where scores from data produced are 0, 1, 2, 3, 4), what is the formula for range?

Answer 9

Xmax - Xmin + 1

Question 10

TRUE OR FALSE: As a measure of variability, the range considers the scores in between the extreme values.

Answer 10

FALSE.

It ignores the scores in between the two extreme values, which is a problem or a disadvantage in using range as a measure of variability.

Question 11

THINK! Why is the range considered to be a crude and unreliable measure of variability?

Answer 11

By virtue of the range, an outlier will make it look like variability is large, even if other scores are clustered close together. In other words, it will make your description of a distribution’s variability inaccurate.