Q: Suppose the number of murders in the U.S. was 16,374 in 2018 and 16,425 in 2019. What is the approximate percent change in the number of murders from 2018 to 2019?

$$\frac{16,425 - 16,374}{16,374} \times 100 \approx 0.31\%$$

Q: In a sample of 150 employees, the 99th percentile of performance scores is 95. If a bonus is paid to each employee with a score at or above the 99th percentile, how many employees will receive the bonus?

Approximately $$0.01 \times 150 = 1.5$$, so 2 employees.

Q: A two-way table shows that 40% of customers who bought Cauliflower also bought Beer, while only 20% of customers who did not buy Cauliflower bought Beer. What is the 'lift' to the purchase of Beer owing to the purchase of Cauliflower?

$$\text{Lift} = \frac{0.40}{0.20} = 2.0$$

Question 1

A bar chart is used to display the number of murders in the United States for 2018 and 2019. The graph shows a much larger bar for 2019 than for 2018, even though the actual increase is less than 10%. Which of the following best explains why this graph is misleading?

Accepted Answer

The y-axis does not start at zero, exaggerating the difference between the two years.

Question 2

Suppose the number of murders in the U.S. was 16,374 in 2018 and 16,425 in 2019. What is the approximate percent change in the number of murders from 2018 to 2019?

Accepted Answer

$$\frac{16,425 - 16,374}{16,374} 	imes 100 \approx 0.31\%$$

Question 3

A histogram is constructed with bins (0.1, 0.2], (0.2, 0.3], (0.3, 0.7] and corresponding frequencies 4, 10, 8 for a sample of size 30. Which of the following is a legitimate histogram with bar widths equal to the bin widths and heights equal to $$\frac{4}{0.1}$$, $$\frac{10}{0.1}$$, $$\frac{8}{0.4}$$?

Accepted Answer

A density histogram, because the area under the bars sums to 1.

Question 4

Suppose a variable $$X is $$approximately normally distributed with mean $$\mu = 4.5$$ and standard deviation $$\sigma = 1.5. $$What is the approximate probability that a randomly selected value of $$X is $$greater than 6.5?

Accepted Answer

$$P(X \u003e 6.5) = P\left(Z \u003e \frac{6.5 - 4.5}{1.5}\right) = P(Z \u003e 1.33) \approx 0.0912$$

Question 5

A diaper manufacturer claims that the population of birthweights for full-term babies is approximately bell-shaped with an average of 7 lbs and a standard deviation of 1.0 lb. What is the approximate fraction of birthweights that are below 5.5 lbs?

Accepted Answer

$$P(X \u003c 5.5) = P\left(Z \u003c \frac{5.5 - 7}{1}\right) = P(Z \u003c -1.5) \approx 0.0668$$

Question 6

In a sample of 150 employees, the 99th percentile of performance scores is 95. If a bonus is paid to each employee with a score at or above the 99th percentile, how many employees will receive the bonus?

Accepted Answer

Approximately $$0.01 	imes 150 = 1.5$$, so 2 employees.

Question 7

Suppose the mean service rating is 4.6 and the standard deviation is 0.7, with ratings ranging from 0 to 5. Which of the following is most likely to be the median of the service ratings?

Accepted Answer

4.6

Question 8

A two-way table shows that 40% of customers who bought Cauliflower also bought Beer, while only 20% of customers who did not buy Cauliflower bought Beer. What is the 'lift' to the purchase of Beer owing to the purchase of Cauliflower?

Accepted Answer

$$	ext{Lift} = \frac{0.40}{0.20} = 2.0$$

Question 9

In a study, the response rate for Drug A among females is 48/250, and for Drug B among females is 158/250. What is the response rate ratio (RR) for Drug A compared to Drug B among females?

Accepted Answer

$$RR = \frac{48/250}{158/250} = \frac{48}{158} \approx 0.304$$

Question 10

Suppose a community has three neighborhoods with mean household incomes of $$150,000, 200$$,000, and $$250,000. Which neighborhood will have the highest number of households with incomes above 250$$,000?

Accepted Answer

The neighborhood with mean income $250,000.

Question 11

Kathy and Jim play golf together for years. Kathy averages 74 with a standard deviation of 3, and Jim averages 97 with a standard deviation of 6. If both are given handicaps so that their handicap-adjusted averages are identical, what is the formula for Kathy's z-score for a round of $$K$$ and Jim's z-score for a round of $$J$$?

Accepted Answer

$$z_K = \frac{K - 74}{3}$$ and $$z_J = \frac{J - 97}{6}$$

Question 12

A sample of 30 data points is grouped into bins of width 0.1, with frequencies 4, 10, and 8. What is the height of the bar for the bin (0.2, 0.3] in a density histogram?

Accepted Answer

$$	ext{Height} = \frac{10}{0.1 	imes 30} = \frac{10}{3} \approx 3.33$$

Question 13

If a variable is approximately normally distributed, which of the following statements is true about the mean, median, and mode?

Accepted Answer

They are all approximately equal.

Question 14

Suppose the 90th percentile of a data set is 150. What does this mean?

Accepted Answer

90% of the data values are less than or equal to 150.

Question 15

A two-way table shows that 30% of customers who bought Cauliflower also bought Beer, and 15% of customers who did not buy Cauliflower bought Beer. What is the rate ratio for Beer purchase given Cauliflower purchase?

Accepted Answer

$$	ext{Rate Ratio} = \frac{0.30}{0.15} = 2.0$$

Question 16

If a data set is strongly right-skewed, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 17

Suppose you are given a data set with the following 5-number summary: 113, 122, 130, 138, 154. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = 138 - 122 = 16$$

Question 18

Which of the following best describes the purpose of a density histogram?

Accepted Answer

To display the proportion of data within each interval, with the total area equal to 1.

Statistics for Business: Study Guide on Data Visualization, Distributions, Percentiles, and Association

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