Q: A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the lower fence for detecting outliers?

$$Q_1 - 1.5$$ \times ($$Q_3$$ - $$Q_1) = 20 - 1.5$$ \times 20 = -10$$

Q: Given a data set with $$Q_1 = 15$, Q_3$ = 25$$, and a value of 40, is 40 an outlier?

Yes, because $$40 \u003e Q_3$ + 1.5 \times (Q_3$ - Q_1$)$$

Question 1

Which formula would you use to calculate the z-score for a value $$x$$ from a population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 2

A manufacturer destroys bolts that are more than 2 standard deviations from the mean length of 8 cm, with a standard deviation of 0.05 cm. What is the minimum length at which a bolt will be destroyed?

Accepted Answer

$$8.10 cm$$

Question 3

If a student’s SAT Math score is in the 74th percentile, what does this mean?

Accepted Answer

74% of students scored the same or lower than this student.

Question 4

Which measure of central tendency and dispersion should be reported for a highly skewed data set with outliers?

Accepted Answer

Median and interquartile range (IQR)

Question 5

Given the five-number summary: 60, 68, 77, 89, 98, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = 89 - 68 = 21$$

Question 6

Which of the following statements about the z-score is TRUE?

Accepted Answer

The z-score is unitless and has mean 0 and standard deviation 1.

Question 7

A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the lower fence for detecting outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes ($$Q_3$$ - $$Q_1) = 20 - 1.5$$ 	imes 20 = -10$$

Question 8

Which boxplot feature indicates a right-skewed distribution?

Accepted Answer

The right whisker is longer than the left whisker.

Question 9

A running back’s 40-yard dash time is 4.37 seconds (mean = 4.50, SD = 0.09). A linebacker’s time is 4.42 seconds (mean = 4.62, SD = 0.12). Who was relatively faster?

Accepted Answer

The linebacker, because his z-score is lower.

Question 10

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

Accepted Answer

Mean

Question 11

If a value is greater than the upper fence in a boxplot, what does this indicate?

Accepted Answer

The value is an outlier.

Question 12

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The range of the middle 50% of the data.

Question 13

A boxplot shows a median closer to $$Q_1$$ and a longer right whisker. What is the likely shape of the distribution?

Accepted Answer

Right-skewed

Question 14

Which of the following steps is NOT required when constructing a box-and-whisker plot?

Accepted Answer

Calculate the mean and standard deviation.

Question 15

Given a data set with $$Q_1 = 15$, Q_3$ = 25$$, and a value of 40, is 40 an outlier?

Accepted Answer

Yes, because $$40 \u003e Q_3$ + 1.5 	imes (Q_3$ - Q_1$)$$

Question 16

Which of the following is the correct interpretation of the 95th percentile of newborn female length being 53.8 cm?

Accepted Answer

95% of newborn females are 53.8 cm or shorter.

Question 17

Which boxplot (I or II) in the image provided likely has the data with a larger standard deviation, and why?

Accepted Answer

Boxplot II, because it has a wider spread.

Question 18

Which of the following is TRUE about quartiles?

Accepted Answer

$$Q_1 is $$the 25th percentile, $$Q_2 is $$the 50th percentile, $$Q_3 is $$the 75th percentile.

Question 19

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

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

Measures of Position, Outliers, and Box Plots in Introductory Statistics

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