Q: A data set has $$Q_1 = 20$, Q_3$ = 40$$, and an outlier is defined as any value more than $$1.5 \times IQR$$ above $$Q_3. $$What is the minimum value that would be considered an outlier on the high end?

$$40 + 1.5 \times (40 - 20) = 70$$

Question 1

A z score is calculated for a student's test score in a class. If the z score is $$-2.15$$, what does this indicate about the student's performance?

Accepted Answer

The student's score is significantly lower than the mean.

Question 2

Given a data set with mean $$\mu = 50$$ and standard deviation $$\sigma = 8$$, what is the z score for a value $$x = 66$$?

Accepted Answer

$$z = \frac{66 - 50}{8} = 2$$

Question 3

Which of the following statements about percentiles is TRUE?

Accepted Answer

The 25th percentile is the same as the first quartile, $$Q_1.$$

Question 4

A wait time of 45 minutes at Space Mountain is in the 72nd percentile. What does this mean?

Accepted Answer

72% of the wait times are less than or equal to 45 minutes.

Question 5

If a data value has a z score of $$2.21$$, how would you classify this value?

Accepted Answer

It is significantly high.

Question 6

Which of the following is NOT part of the 5-number summary?

Accepted Answer

The mean

Question 7

Given the following 5-number summary for wait times (in minutes): 10, 25, 35, 50, 110. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 50 - 25 = 25$$

Question 8

A boxplot is constructed for a data set. If the right whisker is much longer than the left, what does this suggest about the distribution?

Accepted Answer

The distribution is skewed to the right.

Question 9

Which formula is used to calculate the z score for a sample data value $$x$$ with sample mean $$\bar{x}$$ and sample standard deviation $$s$$?

Accepted Answer

$$z = \frac{x - \bar{x}}{s}$$

Question 10

A data set has $$Q_1 = 20$, Q_3$ = 40$$, and an outlier is defined as any value more than $$1.5 	imes IQR$$ above $$Q_3. $$What is the minimum value that would be considered an outlier on the high end?

Accepted Answer

$$40 + 1.5 	imes (40 - 20) = 70$$

Question 11

If the locator $$L$$ for a percentile is not a whole number, what is the correct procedure to find the corresponding data value?

Accepted Answer

Round $$L up to $$the next larger whole number and use that position.

Question 12

Which of the following best describes the median of a data set?

Accepted Answer

It is the value that separates the lower 50% from the upper 50% of the data.

Question 13

A data set of earthquake magnitudes has a mean of $$2.572$$ and a standard deviation of $$0.651. $$What is the z score for an earthquake of magnitude $$4.01$$?

Accepted Answer

$$z = \frac{4.01 - 2.572}{0.651} = 2.21$$

Question 14

Which of the following is TRUE about quartiles?

Accepted Answer

$$Q_2 is $$the same as the median.

Question 15

A modified boxplot is different from a regular boxplot because:

Accepted Answer

It identifies outliers with a special symbol and shortens the whiskers to the most extreme non-outlier values.

Describing, Exploring, and Comparing Data: Measures of Relative Standing and Boxplots

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