Q: For the house price data above, calculate the upper fence using the formula $$Q3 + 1.5 \times IQR. $$What is the value?

$$175 + 1.5 \times (175 - 135) = 235$$

Q: Phillip has a z-score of $$-2.3 in $$vocabulary size. What is his vocabulary size?

$$14000 + (-2.3) \times 3000 = 7100$$

Question 1

Given a dataset of house prices (in thousands of dollars) ordered as follows: 120, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 300, what is the Five Number Summary for this data?

Accepted Answer

$$120, 135, 155, 175, 300$$

Question 2

For the house price data above, calculate the upper fence using the formula $$Q3 + 1.5 	imes IQR. $$What is the value?

Accepted Answer

$$175 + 1.5 	imes (175 - 135) = 235$$

Question 3

Based on the upper fence calculated above, is the maximum house price of $$300 an $$outlier?

Accepted Answer

Yes, because $$300 \u003e 235.$$

Question 4

A histogram of GDP for a dataset is right-skewed with a long tail to the right. Which of the following best describes the distribution?

Accepted Answer

The distribution is positively skewed, with most values clustered at lower GDPs and a few high outliers.

Question 5

Given the summary statistics for family.income.median: mean = $$50,000$$, median = $$48,000$$, standard deviation = $$10,000$$, what can you infer about the distribution?

Accepted Answer

The distribution is likely right-skewed since the mean is greater than the median.

Question 6

The murder rates in the US have a mean $$\mu = 5.9$$ and standard deviation $$\sigma = 5.4. Is $$this data likely to be normal? Use the empirical rule to justify your answer.

Accepted Answer

No, because the standard deviation is almost as large as the mean, suggesting possible skewness or outliers.

Question 7

People's vocabulary sizes are approximately normal with $$\mu = 14000$$ and $$\sigma = 3000. $$According to the empirical rule, what range contains approximately 68% of people's vocabulary sizes?

Accepted Answer

$$14000 \pm 3000$$, or $$11000 to$$ $$17000$$

Question 8

For the same vocabulary distribution, what percentage of people speak less than $$17000$$ words?

Accepted Answer

About 84%, since $$17000 is $$one standard deviation above the mean.

Question 9

What is the z-score for Mary, who speaks $$18800$$ words, given $$\mu = 14000$$ and $$\sigma = 3000$$?

Accepted Answer

$$z = \frac{18800 - 14000}{3000} = 1.6$$

Question 10

Is Mary, with a z-score of $$1.6$$, considered an extreme data point?

Accepted Answer

No, because her z-score is less than 2.

Question 11

Phillip has a z-score of $$-2.3 in $$vocabulary size. What is his vocabulary size?

Accepted Answer

$$14000 + (-2.3) 	imes 3000 = 7100$$

Question 12

Is Phillip, with a z-score of $$-2.3$$, considered an extreme data point?

Accepted Answer

Yes, because his z-score is less than $$-2.$$

Question 13

For a normal distribution with $$\mu = 14000$$ and $$\sigma = 3000$$, what vocabulary size corresponds to the 90th percentile? (Use $$z = 1.28$$ for the 90th percentile.)

Accepted Answer

$$14000 + 1.28 	imes 3000 = 17840$$

Question 14

Which of the following is NOT a condition that must be checked before performing regression analysis?

Accepted Answer

The variables must be qualitative.

Question 15

In a regression analysis predicting college GPA from high school GPA, the $$R^2$$ value is $$0.64. $$What does this mean?

Accepted Answer

64% of the variation in college GPA is explained by high school GPA.

Question 16

A residual plot from a regression analysis shows a clear curved pattern. What does this indicate?

Accepted Answer

The linear model is inappropriate; the relationship is not linear.

Question 17

Which of the following statements about regression analysis is TRUE?

Accepted Answer

A strong correlation does not imply causation.

Question 18

A student has a high school GPA of $$3.1. $$The regression equation predicting college GPA is $$	ext{College GPA} = 0.5 + 0.8 	imes 	ext{High School GPA}. $$What is the predicted college GPA?

Accepted Answer

$$0.5 + 0.8 	imes 3.1 = 2.98$$

Question 19

Which of the following is a reason to use a residual plot in regression analysis?

Accepted Answer

To check for non-linearity and outliers that may not be visible in the scatterplot.

Statistics Review: Five Number Summary, Boxplots, Empirical Rule, Z-scores, Regression, and More

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