Q: A histogram shows the number of days 105 patients were depressed prior to treatment. If 65 patients had fewer than 180 days of depression, what percentage is this?

$$\frac{65}{105} \times 100 = 61.9\%$$

Q: Using the 1.5*IQR criterion for outliers, if $$Q_1 = 37.5$ and Q_3$ = 49.5$$ for actors' ages, what is the upper fence?

$$Q_3 + 1.5$$ \times IQR = 49.5 + 1.5 \times (49.5 - 37.5) = 67.5$$

Q: A boxplot for exam scores has $$Q_1 = 69$, Q_3$ = 79. $$Using the 1.5*IQR criterion, what is the lower fence?

$$Q_1 - 1.5$$ \times IQR = 69 - 1.5 \times (79 - 69) = 54$$

Q: Given the regression equation $$y = 5006 - 491x$$, what is the predicted value of $$y$$ when $$x = 7.5$$?

$$5006 - 491 \times 7.5 = 1413.5$$

Q: A regression equation for predicting mortality rate is $$\text{Mortality} = 49.92 \times \text{Education} + 1493.3. $$What is the predicted mortality rate for a city with an average education level of 10.25 years?

$$49.92 \times 10.25 + 1493.3 = 981.62$$

Question 1

Which of the following variables collected in a survey of college graduates is quantitative?

Accepted Answer

Annual income

Question 2

A researcher collects the following data: annual income, employment status, undergraduate GPA, and zip code. Which variable is qualitative (categorical)?

Accepted Answer

Zip code

Question 3

A histogram of calcium concentrations in drinking water is right-skewed. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median

Question 4

Given the following summary statistics for calcium concentration (ppm): $$	ext{Median} = 172$$, $$	ext{Mean} = 193.5$$, $$	ext{Min} = 34$$, $$	ext{Max} = 419$$, $$Q_1 = 65.4$, Q_3$ = 250$$, what percent of locations had calcium concentrations of 250 ppm and above?

Accepted Answer

25%

Question 5

A histogram shows the number of days 105 patients were depressed prior to treatment. If 65 patients had fewer than 180 days of depression, what percentage is this?

Accepted Answer

$$\frac{65}{105} 	imes 100 = 61.9\%$$

Question 6

Given the frequency table below, how many people made more than 8 phone calls daily?

Number of calls made: 1-4 (16), 5-8 (11), 9-12 (5), 13-16 (3), 17-20 (2)

Accepted Answer

10

Question 7

Using the same frequency table, what is the total number of people surveyed?

Accepted Answer

37

Question 8

In a histogram of tip amounts, the frequencies for each interval are: $$39, 64, 32, 11, 8, 2, 1. $$What is the sample size?

Accepted Answer

$$39 + 64 + 32 + 11 + 8 + 2 + 1 = 157$$

Question 9

Using the 1.5*IQR criterion for outliers, if $$Q_1 = 37.5$ and Q_3$ = 49.5$$ for actors' ages, what is the upper fence?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR = 49.5 + 1.5 	imes (49.5 - 37.5) = 67.5$$

Question 10

A boxplot for exam scores has $$Q_1 = 69$, Q_3$ = 79. $$Using the 1.5*IQR criterion, what is the lower fence?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR = 69 - 1.5 	imes (79 - 69) = 54$$

Question 11

Given the regression equation $$y = 5006 - 491x$$, what is the predicted value of $$y$$ when $$x = 7.5$$?

Accepted Answer

$$5006 - 491 	imes 7.5 = 1413.5$$

Question 12

A regression equation for predicting mortality rate is $$	ext{Mortality} = 49.92 	imes 	ext{Education} + 1493.3. $$What is the predicted mortality rate for a city with an average education level of 10.25 years?

Accepted Answer

$$49.92 	imes 10.25 + 1493.3 = 981.62$$

Question 13

Which of the following best describes the value of the linear correlation coefficient $$r = -0.6405$$?

Accepted Answer

A moderate to strong negative linear relationship

Question 14

Which of the following scatterplots is most likely to have a correlation coefficient $$r = 0.941$$?

Accepted Answer

A scatterplot with points tightly clustered along a positively sloped line

Question 15

Which statement about the linear correlation coefficient $$r is $$FALSE?

Accepted Answer

The linear correlation coefficient $$r is $$expressed in units based on the scale of the explanatory and response variables.

Question 16

A histogram of depression days for 105 patients shows the median is between 140 and 180 days. Which of the following is most likely true?

Accepted Answer

The mean will be larger than the median

Question 17

In a histogram of depression days, 24 patients had 220 or more days of depression out of 105 total. What percentage is this?

Accepted Answer

$$\frac{24}{105} 	imes 100 = 22.9\%$$

Question 18

Which of the following statements about outliers is correct according to the 1.5*IQR rule?

Accepted Answer

An outlier is any value greater than $$Q_3 + 1.5$$ 	imes IQR$$ or less than Q_1$ - 1.5 	imes IQR$$

Statistics Study Guide: Variables, Data Displays, Outliers, and Correlation

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