chapter 3

Question 1

What is the role of statistics in psychological testing?

Answer 1

Summarizes data, compares individual scores, aids in decision-making for education, employment, and clinical diagnosis.

Question 2

Define the Nominal Scale.

Answer 2

Categorizes data without any inherent order.

Question 3

Provide an example of the Nominal Scale.

Answer 3

• Gender (Male, Female, Non-binary)
• Eye color (Blue, Brown, Green)

Question 4

Define the Ordinal Scale.

Answer 4

Ranks data but does not specify equal intervals between ranks.

Question 5

Provide an example of the Ordinal Scale.

Answer 5

• Class ranking (1st, 2nd, 3rd)
• Likert scale responses (Strongly Agree to Strongly Disagree)

Question 6

Define the Interval Scale.

Answer 6

Equal intervals between values but lacks a true zero point.

Question 7

Provide an example of the Interval Scale.

Answer 7

IQ scores.

Question 8

Define the Ratio Scale.

Answer 8

Equal intervals and a true zero point, allowing for meaningful ratios.

Question 9

Provide an example of the Ratio Scale.

Answer 9

Reaction time in milliseconds.

Question 10

What is a frequency distribution?

Answer 10

Arranges test scores to show how often each score occurs.

Question 11

What does a histogram represent?

Answer 11

Graphical representation for continuous data.

Question 12

What does a bar graph represent?

Answer 12

Graphical representation for categorical data.

Question 13

What is the Mean?

Answer 13

Arithmetic average calculated as ( \bar{X} = \frac{\sum X}{n} ).

Question 14

Example calculation of the Mean for scores {50, 60, 70, 80, 90}.

Answer 14

( \bar{X} = 70 ).

Question 15

How is the Median determined?

Answer 15

Middle score if n is odd, average of two middle scores if n is even.

Question 16

What is the Mode?

Answer 16

The most frequent score in a dataset.

Question 17

Define Range.

Answer 17

( \text{Range} = X_{\max} - X_{\min} ).

Question 18

What is the Interquartile Range (IQR)?

Answer 18

( IQR = Q3 - Q1 ).

Question 19

What does Standard Deviation (SD) measure?

Answer 19

The spread of scores around the mean.

Question 20

What is the Empirical Rule related to the Normal Curve?

Answer 20

• 68% of scores within ±1 SD
• 95% within ±2 SD
• 99.7% within ±3 SD

Question 21

What are z-Scores used for?

Answer 21

Allow comparisons across different distributions.

Question 22

How is a z-Score calculated?

Answer 22

( z = \frac{X - \bar{X}}{\sigma} ).

Question 23

What is a T-Score?

Answer 23

Converts z-scores to a scale with a mean of 50 and SD of 10.

Question 24

What does Pearson’s r measure?

Answer 24

The strength and direction of correlation between two variables.

Question 25

What is the range of Pearson’s r?

Answer 25

-1 to +1.

Question 26

What is Skewness?

Answer 26

Describes the asymmetry of a distribution.

Question 27

What does Positive Skew indicate?

Answer 27

Few high scores, tail on the right.

Question 28

What does Negative Skew indicate?

Answer 28

Few low scores, tail on the left.

Question 29

Define Kurtosis.

Answer 29

Describes the peak of a distribution.

Question 30

What is a Leptokurtic distribution?

Answer 30

Tall peak.

Question 31

What is a Platykurtic distribution?

Answer 31

Flat peak.

Question 32

What is a Mesokurtic distribution?

Answer 32

Normal curve.

Question 33

What are the key takeaways from Chapter 3?

Answer 33

* Scales of measurement define how data is categorized. * Central tendency and variability describe distributions. * The normal curve standardizes expectations for performance. * Standard scores and correlation coefficients allow for meaningful comparisons.

Question 34

What is the definition of Mean?

Answer 34

The average of a set of values, calculated by adding all values and dividing by N. ## Footnote N represents the total number of values

Question 35

What does Median refer to in a data set?

Answer 35

The middle value when data is arranged in order. ## Footnote If there is an even number of observations, the median is the average of the two middle numbers.

Question 36

What is the Mode in statistics?

Answer 36

The most frequent value in a data set. ## Footnote A data set may have one mode, more than one mode, or no mode at all.

Question 37

How is Range defined?

Answer 37

The difference between the largest and smallest values in a data set. ## Footnote Calculated as Xmax - Xmin.

Question 38

What does Variance measure?

Answer 38

The average of the squared differences from the Mean. ## Footnote It indicates how much the values in a data set differ from the mean.

Question 39

What is Standard Deviation?

Answer 39

The square root of the variance. ## Footnote It provides a measure of the dispersion of a set of values.

Question 40

What is a z-Score?

Answer 40

A measure of how many standard deviations an element is from the mean. ## Footnote Calculated by subtracting the mean from X and dividing by the standard deviation.

Question 41

What does Correlation (r) indicate?

Answer 41

The strength and direction of a linear relationship between two variables. ## Footnote Pearson's r ranges from -1 to 1.

Question 42

What is the formula for Pearson's r?

Answer 42

Computed step by step using sum of X, Y, XY, X², and Y². ## Footnote It quantifies how two variables relate to each other.

Question 43

What is a t-test used for?

Answer 43

To compare the means of two groups. ## Footnote It helps determine if there is a significant difference between the groups.

Question 44

Fill in the blank: To find the mean, you must _______.

Answer 44

Add all values, divide by N. ## Footnote N is the total number of values in the data set.

Question 45

Fill in the blank: To find the median, you must _______.

Answer 45

Arrange data, find middle score. ## Footnote This ensures you accurately identify the central value.

Question 46

Fill in the blank: To identify the mode, you must _______.

Answer 46

Identify highest frequency score. ## Footnote This means finding the value that appears most often.

Question 47

Fill in the blank: To calculate variance, you must _______.

Answer 47

Find mean, subtract from each score, square, sum, divide. ## Footnote This process quantifies the variability of data.

Question 48

Fill in the blank: To calculate standard deviation, you must _______.

Answer 48

Take square root of variance. ## Footnote This gives a more interpretable measure of dispersion.

Question 49

Fill in the blank: To compute a z-Score, you must _______.

Answer 49

Subtract mean from X, divide by SD. ## Footnote This standardizes the score relative to the mean.