Q: A dataset has $$Q_1 = 735$, Q_3$ = 4668$$, and $$IQR = 3933. $$What is the upper fence for identifying outliers?

$$Q_3 + 1.5$$ \times IQR = 10,567.5$$

Q: Which of the following is the correct formula for a $$z-$$score?

$$z = \frac{\text{value} - \text{mean}}{\text{standard deviation}}$$

Question 1

Given the following exam scores: 82, 77, 90, 71, 62, 68, 74, 84, 94, 88, what is the mean (average) score? Use the formula $$\mu = \frac{\sum x_i}{N}.$$

Accepted Answer

$$\mu = 79$$

Question 2

Which measure of center is most resistant to outliers in a dataset?

Accepted Answer

Median

Question 3

A dataset of phone call lengths is: 7, 4, 1, 4, 3, 48, 5, 3, 6. Which measure best describes the typical phone call length?

Accepted Answer

Median

Question 4

What is the formula for the sample standard deviation $$s$$?

Accepted Answer

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

Question 5

If a dataset is skewed right, which of the following is true about the mean and median?

Accepted Answer

Mean \u003e Median

Question 6

A student scores 73 on two different exams. On the first exam, the mean is 72 and the standard deviation is 9. On the second, the mean is 64 and the standard deviation is 2. Which exam did the student perform better on relative to the class?

Accepted Answer

Second exam

Question 7

What is the interquartile range (IQR) if $$Q_1 = 735$ and Q_3$ = 4668$$?

Accepted Answer

$$IQR = 3933$$

Question 8

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to outliers.

Question 9

According to the Empirical Rule, what percentage of data falls within two standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

95%

Question 10

If a value has a $$z-$$score of 2.5, what does this indicate?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Question 11

A dataset has $$Q_1 = 735$, Q_3$ = 4668$$, and $$IQR = 3933. $$What is the upper fence for identifying outliers?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR = 10,567.5$$

Question 12

Which of the following is the correct formula for a $$z-$$score?

Accepted Answer

$$z = \frac{	ext{value} - 	ext{mean}}{	ext{standard deviation}}$$

Question 13

If the range of a dataset is 32, and the minimum value is 62, what is the maximum value?

Accepted Answer

94

Question 14

Which of the following best describes the mode?

Accepted Answer

The most frequently observed value.

Question 15

A five-number summary consists of which of the following values?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 16

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

Accepted Answer

The student scored higher than 74% of test-takers.

Question 17

Which measure of dispersion is resistant to outliers?

Accepted Answer

Interquartile range (IQR)

Question 18

According to Chebyshev’s Inequality, at least what percent of data falls within $$k=2$$ standard deviations of the mean for any dataset?

Accepted Answer

75%

Question 19

Which of the following is NOT true about measures of dispersion?

Accepted Answer

They can be negative.

Question 20

If a dataset has a mean of 100 and a standard deviation of 15, what is the $$z-$$score for a value of 130?

Accepted Answer

$$z = 2$$

Numerical Summaries of Data: Measures of Center, Dispersion, and Position

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