Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A researcher wants to estimate the average height of all adult men in a city. She randomly selects 200 men and calculates their average height. In this context, what is the population, and what is the sample?

Accepted Answer

Population: All adult men in the city; Sample: 200 randomly selected men

Question 3

Which of the following variables is quantitative and discrete?

Accepted Answer

The number of pets a person owns

Question 4

A bar chart and a histogram both use bars to display data. Which statement correctly distinguishes between them?

Accepted Answer

A bar chart displays frequencies for categories, while a histogram displays frequencies for intervals of quantitative data.

Question 5

Given the following data set: 2, 4, 4, 5, 7, what is the mean?

Accepted Answer

$$\frac{2+4+4+5+7}{5} = 4.4$$

Question 6

Which measure of center is most resistant to outliers?

Accepted Answer

Median

Question 7

A distribution is right-skewed. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 8

The standard deviation of a data set is calculated as:

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 9

If a value has a z-score of $$-2.5$$, what does this indicate?

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 10

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 11

A boxplot displays which of the following summary statistics?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 12

Given the data set: 1, 2, 3, 4, 6, 8, 9, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 8 - 2 = 6$$

Question 13

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to outliers.

Question 14

A survey asks people to report their favorite type of music. Which type of variable is this?

Accepted Answer

Categorical, nominal

Question 15

Which of the following best describes the modal category in a frequency table?

Accepted Answer

The category with the largest frequency

Question 16

A researcher finds that the mean income in a sample is much higher than the median income. What does this suggest about the distribution of incomes?

Accepted Answer

The distribution is right-skewed.

Question 17

Which of the following is the correct formula for a z-score?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 18

If the lower quartile $$Q_1 is 20 $$and the upper quartile $$Q_3 is 40$$, what is the lower fence for detecting outliers using the 1.5 x IQR rule?

Accepted Answer

$$Q_1 - 1.5$$ 	imes ($$Q_3$$ - $$Q_1) = 20 - 1.5$$ 	imes 20 = -10$$

Question 19

Which of the following graphs would be most appropriate for displaying the distribution of a categorical variable such as 'favorite ice cream flavor'?

Accepted Answer

Pie chart

Gathering and Exploring Data: Foundations of Statistical Analysis

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