Q: A data set has $$Q_1 = 28$, Q_3$ = 38. $$What is the upper fence for outliers?

$$UF = Q_3$ + 1.5(IQR) = 38 + 1.5 \times 10 = 53$$

Question 1

Which formula correctly calculates the z-score for a sample data value $$x$$ with sample mean $$\overline{x}$$ and sample standard deviation $$s$$?

Accepted Answer

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

Question 2

A student scored 88 on an exam where the mean was 73.2 and the standard deviation was 8.5. What is the student's z-score?

Accepted Answer

$$z = \frac{88 - 73.2}{8.5} = 1.74$$

Question 3

According to the Empirical Rule, approximately what percentage of data values in a bell-shaped distribution have z-scores between -2 and 2?

Accepted Answer

95%

Question 4

If a data value has a z-score of -1.5, how does it compare to the mean?

Accepted Answer

It is 1.5 standard deviations below the mean.

Question 5

A student’s SAT score is in the 74th percentile. What does this mean?

Accepted Answer

74% of students scored less than or equal to this student.

Question 6

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

Accepted Answer

Mean

Question 7

Given a data set with $$Q_1 = 21$ and Q_3$ = 38$$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 17$$

Question 8

Which formula is used to calculate the lower fence for detecting outliers using the IQR method?

Accepted Answer

$$LF = Q_1$ - 1.5(IQR)$$

Question 9

A data set has $$Q_1 = 28$, Q_3$ = 38. $$What is the upper fence for outliers?

Accepted Answer

$$UF = Q_3$ + 1.5(IQR) = 38 + 1.5 	imes 10 = 53$$

Question 10

Which statement best describes the interquartile range (IQR)?

Accepted Answer

It is the range of the middle 50% of the data.

Question 11

If a new extreme value is added to a data set, which measure is most likely to be affected the least?

Accepted Answer

Median

Question 12

Which of the following is true about the median and IQR?

Accepted Answer

Both are resistant to outliers.

Question 13

A boxplot is constructed for a data set. What does an asterisk (*) outside the whiskers represent?

Accepted Answer

An outlier.

Question 14

Which of the following best describes the shape of a distribution if the boxplot shows a longer whisker on the left and the median is closer to $$Q_3$$?

Accepted Answer

Skewed left

Question 15

Given the data set: 5, 15, 16, 20, 21, 25, 26, 27, 30, 30, 31, 32, 32, 34, 35, 38, 38, 41, 43, 77. If $$Q_1 = 21$, Q_3$ = 38$$, and $$IQR = 17$$, which value is an outlier?

Accepted Answer

77

Question 16

Which step is NOT part of constructing a boxplot?

Accepted Answer

Calculate the mean and standard deviation.

Question 17

If a data value is less than the lower fence or greater than the upper fence, what is it considered?

Accepted Answer

An outlier

Question 18

Which of the following is the correct five-number summary for the data set: 6.5%, 9.9%, 12.0%, 13.0%, 13.3%, 13.9%, 14.3%, 14.4%, 14.4%, 14.5%?

Accepted Answer

6.5%, 12.0%, 13.6%, 14.4%, 14.5%

Question 19

Which of the following statements about quartiles is correct?

Accepted Answer

$$Q_3 is $$the 75th percentile.

Measures of Position and Outliers: Z-scores, Percentiles, Quartiles, IQR, Outliers, Five-Number Summary, and Boxplots

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