Q: Which of the following is a potential outlier according to the 1.5 x IQR rule for the cereal sodium data (Q1 = 145, Q3 = 225, IQR = 80)?

A value less than $$145 - 1.5 \times 80 = 25 or $$greater than $$225 + 1.5 \times 80 = 345$$

Question 1

Which of the following is the correct formula for the sample mean $$\bar{x} of a $$data set with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 2

A sociologist wants to summarize the 'typical' family income in a city with a few extremely wealthy families. Which measure of center should they use and why?

Accepted Answer

Median, because it is resistant to outliers.

Question 3

Given the following sodium values (mg) for 20 cereals: min = 0, Q1 = 145, median = 200, Q3 = 225, max = 290. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 225 - 145 = 80$$

Question 4

Which of the following statements about the standard deviation $$s is $$TRUE?

Accepted Answer

$$s is $$not resistant to outliers.

Question 5

A distribution of exam scores is right-skewed. Which measure of center is most appropriate to describe a 'typical' score?

Accepted Answer

Median

Question 6

If a data set has a mean of $$50$$ and a standard deviation of $$5$$, what is the z-score for a value of $$60$$?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 7

Which of the following is NOT part of the five-number summary?

Accepted Answer

Standard deviation

Question 8

According to the Empirical Rule, for a bell-shaped distribution, approximately what percent of observations fall within two standard deviations of the mean?

Accepted Answer

95%

Question 9

A boxplot is most useful for which of the following tasks?

Accepted Answer

Comparing the spread and center of two or more distributions

Question 10

Which of the following is a potential outlier according to the 1.5 x IQR rule for the cereal sodium data (Q1 = 145, Q3 = 225, IQR = 80)?

Accepted Answer

A value less than $$145 - 1.5 	imes 80 = 25 or $$greater than $$225 + 1.5 	imes 80 = 345$$

Question 11

Which of the following best describes a mode?

Accepted Answer

The value that occurs most often in a data set

Question 12

A city government wants to estimate the total tax base using citizens' incomes, which are right-skewed. Which measure should they use?

Accepted Answer

Mean, because it reflects the total sum of incomes.

Question 13

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

Accepted Answer

Label both axes and provide proper headings.

Question 14

If all values in a data set are the same, what is the value of the standard deviation $$s$$?

Accepted Answer

$$s = 0$$

Question 15

Which of the following is TRUE about the relationship between mean and median in a left-skewed distribution?

Accepted Answer

The mean is less than the median.

Question 16

A histogram of survival times for Disease X is shown to be symmetric. Which measure(s) of center and spread are most appropriate to summarize the data?

Accepted Answer

Mean and standard deviation

Question 17

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

Accepted Answer

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

Question 18

Which of the following is a property of the variance $$s^2$$?

Accepted Answer

It is measured in squared units of the original data.

Question 19

A student claims that the range is a resistant measure of spread. Is this correct? Why or why not?

Accepted Answer

No, because the range is strongly affected by outliers.

Exploring Data with Graphs and Numerical Summaries

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