Question 1

Which of the following best describes the main purpose of descriptive statistics?

Accepted Answer

To summarize and organize data collected from a study.

Question 2

Which scale of measurement is most appropriate for categorizing students by their favorite color?

Accepted Answer

Nominal

Question 3

A researcher records the finishing positions (1st, 2nd, 3rd, etc.) of runners in a race. What scale of measurement is being used?

Accepted Answer

Ordinal

Question 4

Which of the following is a key difference between interval and ratio scales?

Accepted Answer

Ratio scales have an absolute zero, interval scales do not.

Question 5

Which measure of central tendency is most appropriate for data measured on a nominal scale?

Accepted Answer

Mode

Question 6

Given the following scores: 2, 4, 4, 6, 8, what is the mean?

Accepted Answer

$$ \frac{2+4+4+6+8}{5} = 4.8 $$

Question 7

A distribution of exam scores is highly skewed to the right (positively skewed). Which measure of central tendency is likely to be the highest?

Accepted Answer

Mean

Question 8

Which of the following is NOT a characteristic of the nominal scale?

Accepted Answer

Numerical operations can be performed.

Question 9

What is the formula for the variance of a population?

Accepted Answer

$$ \$$sigma^2$$ = \frac{SS}{N} $$

Question 10

Why is the denominator $$ n-1 $$ used instead of $$ n $$ when calculating the sample variance?

Accepted Answer

It corrects for bias and provides a better estimate of population variance.

Question 11

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The range of the middle 50% of scores.

Question 12

A psychologist wants to compare the average reaction times of two groups. Which measure of central tendency should she use if the data are measured on a ratio scale?

Accepted Answer

Mean

Question 13

Which type of graph is most appropriate for displaying the frequency distribution of categorical (nominal) data?

Accepted Answer

Bar graph

Question 14

If a frequency distribution table shows a cumulative frequency of 40 for a class interval and the total frequency is 50, what is the cumulative proportion for that class?

Accepted Answer

$$ \frac{40}{50} = 0.8 $$

Question 15

Which of the following is a property of the standard deviation?

Accepted Answer

It is the square root of the variance.

Question 16

A researcher collects the following data: 5, 7, 7, 8, 10. What is the median?

Accepted Answer

7

Question 17

Which of the following best explains why the mean is not always the best measure of central tendency for a highly skewed distribution?

Accepted Answer

The mean is influenced by extreme values (outliers).

Question 18

Which formula would you use to calculate the sum of squares (SS) using the definition formula?

Accepted Answer

$$ SS = \sum (X - \overline{X})^2$ $$

Question 19

Which of the following is NOT a reason for constructing frequency distributions?

Accepted Answer

To make inferences about a population.

Descriptive Statistics: Foundations, Data Types, and Data Summarization

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