Module 2: Textbook

Question 1

frequency table

In terms of levels

Answer 1

a table showing levels of a variable together with the frequency associated with each level.

Question 2

Bimodal

Answer 2

A bimodal distribution is one with two equal or approximately equally high value frequencies. Note that a distribution with two distinct peaks is not considered bimodal unless the peaks are very nearly equal.

Question 3

Multimodal

Answer 3

A multimodal distribution is one with multiple, approximately equal peaks. A bimodal distribution could be considered as a special case of a multimodal distribution.

Question 4

Skewness in data is a result of

Answer 4

Having outliers in the data, i.e., data values that have the effect of extending the tail of the distribution in one direction or the other.

Question 5

Negative skew happens when the mass of the distribution is concentrated on the —- of the figure. It has relatively few — values. The distribution is said to be —skewed or negatively skewed.

Answer 5

• right
• low
• left

Question 6

Positive skew happens when the mass of the distribution is concentrated on the — of the figure. It has relatively few —- values. The distribution is —skewed or positively skewed.

Answer 6

• left
• high
• right

Question 7

Skewness can also be a result of either a——

Answer 7

floor effect or a ceiling effect

Question 8

A floor effect (3)

piles on+results in+ex

Answer 8

occurs when values pile up against some lower limit, resulting in a positive skew, for example, as in the case of an exam that is too difficult for the target population.

Question 9

A ceiling effect

piles on+results in+ex

Answer 9

occurs when values pile up against some upper limit, resulting in a negative skew, for example, as in the case of an exam that is too easy so that most testers score very high.

Question 10

In the example above, notice how the —- and — are “pulled” to one side of the peak in the direction of the skew. Both are affected by extreme values in the distribution; the — is the most sensitive to outliers, or extreme values, in a distribution.

Answer 10

• median
• mean
• mean

Question 11

Explain how to determine the Mean of a Grouped Data Set

Answer 11

Question 12

The two most-used measures of dispersion, or variability, are the ——

Answer 12

variance and the standard deviation.

Question 13

If the entire population of values is given, deviation is represented as

Answer 13

(x – μ), the distance between a raw value x and the population mean, mu

Question 14

If the distribution is a subset of values, as in a sample, deviation is represented as

Answer 14

(x – x̅), the distance between a raw value x and the sample mean, x-bar

Question 15

The sum of deviations from the mean in a distribution always equals —-. Because —-

Answer 15

• zero
• since the mean is the average of the values in the distribution, the differences between the mean and values above the mean will be offset by the differences below the mean.

Question 16

Difference between variance and SD

Answer 16

Standard deviation is a measure of dispersion of a cluster of data from the center, whereas deviation refers to the amount by which a single data point differs from a fixed value.

Question 17

variance

in terms of SD

Answer 17

the average of the squared deviations from the mean. If the values for the entire population are known, the population variance is calculated using N to represent the total number of values in the population.

Question 18

There are two reasons for squaring the deviations used in calculating the variance:

Answer 18

• Squaring “weights” the value in favor of the larger deviations, increases the effect of “outliers” in the distribution.
• Squaring makes all the values positive.

Question 19

The standard deviation is defined as (2)

in terms of variance

Answer 19

the principal square root of the variance. Taking the square root returns the value to the original scale of measurement so that it is expressed in units of the original data set.

Question 20

Since it is expressed in units of the original data set, the standard deviation summarizes variability in a distribution in a form that is —–. It also serves as a —- for values in the distribution.

Answer 20

• specific to that particular distribution
• locator

Question 21

Since a z-score represents the distance a data point is from the mean of the distribution, calculating a z-score is simply a matter of

Answer 21

dividing the difference between the data point and the mean by the calculated standard deviation of the distribution. This tells you the number of standard deviations the score is away from the mean.

Question 22

A negative z-score indicates the associated raw data value is —– the mean, and a positive z-score is associated with a value that is —- the mean.

Answer 22

• below
• above