Question 1

Which of the following best describes the 'Five W's and one H' approach in statistics?

Accepted Answer

A framework for summarizing the key aspects of data: Who, What, When, Where, Why, and How.

Question 2

A researcher collects data on the number of hours students study per week and their exam scores. Which variable is most likely to be considered the 'response variable'?

Accepted Answer

The exam scores.

Question 3

Which of the following is an example of a categorical variable?

Accepted Answer

Type of car (sedan, SUV, truck)

Question 4

A pie chart is most appropriate for displaying:

Accepted Answer

The proportions of categories in a categorical variable.

Question 5

Which of the following statements about histograms is TRUE?

Accepted Answer

Histograms display the frequency of data within equal-width intervals for quantitative data.

Question 6

Given the following data set: 2, 4, 4, 6, 8, what is the median?

Accepted Answer

$4$

Question 7

Which measure of center is most affected by outliers?

Accepted Answer

Mean

Question 8

A boxplot is constructed for the following data: 5, 7, 8, 12, 15, 18, 20. What is the interquartile range (IQR)?

Accepted Answer

$8$

Question 9

Which of the following best describes the standard deviation?

Accepted Answer

The square root of the average squared deviation from the mean.

Question 10

If a dataset is skewed to the right, which of the following is most likely TRUE?

Accepted Answer

The mean is greater than the median.

Question 11

Which transformation can be used to make a right-skewed dataset more symmetric?

Accepted Answer

Taking the log base 10 of each value.

Question 12

Suppose the heights of adult men are normally distributed with mean $\mu = 70$ inches and standard deviation $\sigma = 3$ inches. What is the $z$-score for a man who is 76 inches tall?

Accepted Answer

$z = 2$

Question 13

Which of the following statements about the normal model is FALSE?

Accepted Answer

The normal model is appropriate for all types of data, including categorical data.

Question 14

A researcher wants to compare the test scores of two different classes. Which summary statistics should they use to compare the center and spread of the distributions?

Accepted Answer

Mean and standard deviation, or median and interquartile range.

Question 15

Which of the following is NOT a step in constructing a boxplot?

Accepted Answer

Plot the mean as a central line.

Question 16

If you standardize every value in a dataset by subtracting the mean and dividing by the standard deviation, what will be the mean and standard deviation of the resulting $z$-scores?

Accepted Answer

Mean $= 0$, Standard deviation $= 1$

Question 17

Which of the following best describes an outlier in a dataset?

Accepted Answer

A value that is much higher or lower than most of the other values.

Question 18

A stem-and-leaf plot is most useful for:

Accepted Answer

Displaying the distribution of a small quantitative dataset while preserving individual values.

Question 19

Which of the following is a correct formula for the sample standard deviation $s$ of $n$ values $x_1, x_2, ..., x_n$ with sample mean $\overline{x}$?

Accepted Answer

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}$

Question 20

A dataset has a mean of 50 and a standard deviation of 5. If every value in the dataset is increased by 10, what will be the new mean and standard deviation?

Accepted Answer

Mean $= 60$, Standard deviation $= 5$

Foundations of Statistics: Data, Distributions, and the Normal Model

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