Chapter 4

Question 1

Variability

Answer 1

it simply means that things aren’t always the same; they vary.

• Variability 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.

Question 2

a good measure of variability serves two purposes:

Answer 2

• Variability describes the distribution. Specifically, it tells whether the scores are clustered close together or are spread out over a large distance - It tells how much distance to expect between one score and another
• Variability measures how well an individual score (or group of scores) represents the entire distribution.

Question 3

range

Answer 3

the distance covered by the scores in a distribution, from the smallest score to the largest score.
range = X (max) - X (min)

When the scores are measurements of a continuous variable:
range = upper real limit for X max - lower real limit for X min

When the scores are whole numbers, the range can also be defined as the number of measurement categories:
range = X max - X min + 1

Question 4

standard deviation

Answer 4

provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered.

Question 5

Deviation

Answer 5

distance from the mean:

deviation score = X - mu (mean)

Question 6

Deviation score

Answer 6

he distance (and direction) from the mean to a specific score.

deviation score = X - mu (mean)

Question 7

how to find standard deviation

Answer 7

1. calculate deviation score
2. calculate the mean of the deviation scores (first add up deviation scores than divide by N)
3. get rid of the signs (+ and -). The standard procedure for accomplishing this is to square each deviation score. Using the squared values, you then compute the mean squared deviation, which is called variance.
4. The final step simply takes the square root of the variance to obtain the standard deviation, which measures the standard distance from the mean.

Question 8

Variance

Answer 8

Variance equals the mean of the squared deviations. Variance is the average squared distance from the mean.

Question 9

Standard deviation

Answer 9

Standard deviation is the square root of the variance and provides a measure of the standard, or average distance from the mean.

Standard deviation = Square root of Variance

Question 10

Variance

Answer 10

Variance = mean squared deviation = sum of squared deviations/number of scores

Question 11

SS, or sum of squares

Answer 11

SS, or sum of squares, is the sum of the squared deviation scores.

Question 12

Definitional formula (to compute SS)

Answer 12

SS = sigma(X-mu)^2

(use when mean is a whole number)

Question 13

Computational formula (to compute SS)

Answer 13

SS = sigmaX^2 - (sigmaX)^2 / N

(use when mean is not a whole number)

Question 14

Variance equation using SS

Answer 14

Variance = SS/N

Question 15

Standard deviation equation using SS

Answer 15

standard deviation = square root of SS/N

Question 16

Population variance

Answer 16

The average squared distance from the mean; the mean of the squared deviations.

o^2 = SS/N

Question 17

Population standard deviation

Answer 17

Population standard deviation is represented by the symbol o and equals the square root of the population variance.

o = square root of SS/N

Question 18

Definitional formula for sum of squared deviation for a sample

Answer 18

SS = sigma(X-M)^2

Question 19

Computational formula for sum of squared deviation for a sample

Answer 19

SS = sigmaX^2 - (sigmaX)^2 / n

Question 20

sample variance

Answer 20

The sum of the squared deviations divided by df = n-1. An unbiased estimate of the population variance.

Sample variance is represented by the symbol s^2 and equals the mean squared distance from the mean. Sample variance is obtained by dividing the sum of squares by n − 1.

s^2 = SS/n-1

Question 21

Sample standard deviation

Answer 21

Sample standard deviation is represented by the symbol s and equal the square root of the sample variance.

s = square root of s^2 = square root of SS/n-1

Question 22

degrees of freedom, or df

Answer 22

For a sample of n scores, the degrees of freedom, or df , for the sample variance are defined as df = n-1 . The degrees of freedom determine the number of scores in the sample that are independent and free to vary.

Question 23

unbiased

Answer 23

A statistic that, on average, provides an accurate estimate of the corresponding population parameter. The sample mean and sample variance are unbiased statistics.

• A sample statistic is unbiased if the average value of the statistic is equal to the population parameter. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n.)

Question 24

biased

Answer 24

A sample statistic is biased if the average value of the statistic either underestimates or overestimates the corresponding population parameter.

Question 25

Presenting mean and standard deviation in a graph

Answer 25

• In frequency distribution graphs, we identify the position of the mean by drawing a vertical line
• Because the standard deviation measures distance from the mean, it is represented by a line or an arrow drawn from the mean outward for a distance equal to the standard deviation

Question 26

Transformation of scales

Answer 26

• Adding a constant to each score does not change the standard deviation
• Multiplying each score by a constant causes the standard deviation to be multiplied by the same constant.

Question 27

low variability

Answer 27

existing patterns can be seen clearly

Question 28

high variability

Answer 28

high variability tends to obscure any patterns that might exist

Question 29

error variance

Answer 29

the variance that exists in a set of sample data is often classified as error variance

• This term is used to indicate that the sample variance represents unexplained and uncontrolled differences between scores. As the error variance increases, it becomes more difficult to see any systematic differences or patterns that might exist in the data.

Question 30

What symbols are used for the mean and standard deviation for a sample in a research report?

Answer 30

The mean is identified by the letter M and the standard deviation is represented by SD.