Q: Given the following sodium values (mg) for 20 breakfast cereals: 0, 70, 125, 125, 140, 150, 170, 180, 180, 200, 200, 210, 210, 220, 220, 225, 230, 250, 260, 290, what is the interquartile range (IQR)?

$$\text{IQR} = Q_3$ - Q_1$ = 225 - 145 = 80$$

Q: A value is considered a potential outlier if it is:

More than $$1.5 \times \text{IQR}$$ above $$Q_3 or $$below $$Q_1$$

Question 1

Which of the following statements best explains why the median is considered a resistant measure of center, while the mean is not?

Accepted Answer

The median is not affected by extreme values (outliers), while the mean is pulled toward them.

Question 2

Given the following sodium values (mg) for 20 breakfast cereals: 0, 70, 125, 125, 140, 150, 170, 180, 180, 200, 200, 210, 210, 220, 220, 225, 230, 250, 260, 290, what is the interquartile range (IQR)?

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$ = 225 - 145 = 80$$

Question 3

A distribution of exam scores is bell-shaped with a mean of 70 and a standard deviation of 8. According to the Empirical Rule, approximately what percentage of students scored between 54 and 86?

Accepted Answer

About 95%

Question 4

Which of the following is NOT a component of the five-number summary?

Accepted Answer

Mean

Question 5

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

Accepted Answer

Mean, because it accounts for all values and is appropriate for estimating totals.

Question 6

If a data set has a mean of 50 and a standard deviation of 5, what is the z-score for an observation of 65?

Accepted Answer

$$z = \frac{65 - 50}{5} = 3$$

Question 7

Which of the following best describes the effect of a strong right skew on the mean and median?

Accepted Answer

The mean is greater than the median.

Question 8

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

Accepted Answer

Mean and standard deviation

Question 9

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

Accepted Answer

Label both axes and provide proper headings.

Question 10

Given a data set with $$n = 7$$ values: 2, 4, 6, 8, 10, 12, 100, which measure of center is most affected by the outlier (100)?

Accepted Answer

Mean

Question 11

If the range of a data set is 50 and the minimum value is 20, what is the maximum value?

Accepted Answer

70

Question 12

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

Accepted Answer

Comparing the spread and center of two or more distributions

Question 13

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

Accepted Answer

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

Question 14

A value is considered a potential outlier if it is:

Accepted Answer

More than $$1.5 	imes 	ext{IQR}$$ above $$Q_3 or $$below $$Q_1$$

Question 15

Which of the following best describes the mode?

Accepted Answer

The value that occurs most often in a data set

Question 16

If a distribution is left-skewed, which of the following is true?

Accepted Answer

The mean is less than the median.

Question 17

Which summary statistic is most appropriate for describing the spread of a strongly skewed distribution with outliers?

Accepted Answer

Interquartile range (IQR)

Question 18

A student claims that the standard deviation can never be zero. Is this correct? Why or why not?

Accepted Answer

Incorrect. The standard deviation is zero only when all observations are the same.

Question 19

Which of the following is a potential misuse of graphical summaries?

Accepted Answer

Using pictograms with misleading proportions to exaggerate differences

Lesson 4

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