Q: A data set has a minimum value of 10, first quartile $$Q_1 = 15$, median = 20, third quartile Q_3$ = 25$$, and maximum value of 40. Which value would be considered a potential outlier?

40, because it is more than $$Q_3 + 1.5$$ \times IQR$$

Q: A z-score is calculated as:

$$z = \frac{\text{observation} - \text{mean}}{\text{standard deviation}}$$

Question 1

A city government wants to estimate the total tax base by summarizing the incomes of its citizens. The income data is right-skewed due to a few extremely high earners. Which measure of center should the city use, and why?

Accepted Answer

The mean, because it reflects the total sum of all incomes.

Question 2

Given the following data set of CO$$_2$$ pollution levels (in metric tons per person): 23, 11, 19.7, 9.8, 1.8, 1.2, 0.7, 0.2, what is the mean?

Accepted Answer

Question 3

Which of the following statements about the mean and median is TRUE for a right-skewed distribution?

Accepted Answer

The mean is greater than the median.

Question 4

A data set contains the following values: 2, 4, 4, 4, 5, 7, 9. What is the mode?

Accepted Answer

4

Question 5

Which measure of center is considered resistant to outliers?

Accepted Answer

Median

Question 6

A researcher is analyzing the salaries of employees at a tech company. The data is highly skewed due to a few executives earning much more than the rest. Which summary should the researcher use to describe a 'typical' salary?

Accepted Answer

Median

Question 7

Given the data set: 3, 7, 8, 12, 13, 14, 18, 21, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 16 - 7.5 = 8.5$$

Question 8

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

Accepted Answer

It is resistant to outliers.

Question 9

A set of exam scores is approximately bell-shaped with a mean of 70 and a standard deviation of 5. According to the Empirical Rule, about what percentage of scores fall between 60 and 80?

Accepted Answer

About 68%

Question 10

Which of the following is the correct formula for the sample standard deviation $$s$$?

Accepted Answer

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

Question 11

A data set has a minimum value of 10, first quartile $$Q_1 = 15$, median = 20, third quartile Q_3$ = 25$$, and maximum value of 40. Which value would be considered a potential outlier?

Accepted Answer

40, because it is more than $$Q_3 + 1.5$$ 	imes IQR$$

Question 12

If a data set has all values equal, what is the value of the standard deviation?

Accepted Answer

0

Question 13

A z-score is calculated as:

Accepted Answer

$$z = \frac{	ext{observation} - 	ext{mean}}{	ext{standard deviation}}$$

Question 14

Which of the following is NOT included in the five-number summary?

Accepted Answer

Mean

Question 15

A boxplot is most useful for:

Accepted Answer

Comparing the spread and center of two or more distributions

Question 16

Which of the following is a guideline for constructing effective graphs?

Accepted Answer

Label both axes and start the vertical axis at 0

Question 17

If a data set is strongly skewed with outliers, which summary is most appropriate?

Accepted Answer

Five-number summary

Question 18

A student calculates the range of a data set as 50. What does this value represent?

Accepted Answer

The difference between the largest and smallest values

Question 19

Which of the following statements about the mode is correct?

Accepted Answer

It is the value that occurs most often in the data set

Question 20

A data set has $$Q_1 = 20$, Q_3$ = 40. $$Which value would be considered a potential outlier according to the 1.5 x IQR rule?

Accepted Answer

A value less than $$Q_1 - 1.5$$ 	imes ($$Q_3$$ - $$Q_1) = 20 - 1.5$$ 	imes 20 = -10$$

Exploring Data with Graphs and Numerical Summaries

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