Q: A credit card company uses the upper fence to flag possible fraud. If $$Q_3 = 138$, $$IQR = 54$$, what is the upper fence?

$$UF = Q_3$ + 1.5 \times IQR = 138 + 1.5 \times 54 = 219$$

Question 1

Which of the following best describes the difference between the population mean and the sample mean?

Accepted Answer

The population mean is a parameter, while the sample mean is a statistic.

Question 2

Given the following exam scores for a class: 62, 68, 71, 74, 77, 82, 84, 88, 90, 94. What is the median score?

Accepted Answer

$$M = \frac{77 + 82}{2} = 79.5$$

Question 3

A data set has a mean of 100 and a standard deviation of 16.1. According to the Empirical Rule, approximately what percentage of data falls between 67.8 and 132.2?

Accepted Answer

About 95%

Question 4

Which measure of central tendency is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 5

A student scored 88 on a test where the mean was 78 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = \frac{88 - 78}{5} = 2.0$$

Question 6

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

Accepted Answer

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

Question 7

A set of ride-share distances has $$Q_1 = 2.2$ miles, Q_3$ = 9.4$$ miles. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 7.2$$ miles

Question 8

If a distribution is skewed right, which measure of center is most appropriate to report?

Accepted Answer

Median

Question 9

A frequency distribution has midpoints $$x_i$$ and frequencies $$f_i. $$Which formula gives the approximate mean?

Accepted Answer

$$\mu = \frac{\sum x_i f_i}{\sum f_i}$$

Question 10

Which of the following is NOT a step in constructing a boxplot?

Accepted Answer

Calculate the mean and standard deviation.

Question 11

A credit card company uses the upper fence to flag possible fraud. If $$Q_3 = 138$, $$IQR = 54$$, what is the upper fence?

Accepted Answer

$$UF = Q_3$ + 1.5 	imes IQR = 138 + 1.5 	imes 54 = 219$$

Question 12

Which of the following statements about Chebyshev’s Inequality is correct?

Accepted Answer

It applies to any data set, regardless of shape.

Question 13

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

Accepted Answer

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

Question 14

Which of the following is the correct formula for the population variance?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x_i - \mu)^2$}{N}$$

Question 15

If a data set has two modes, how is it described?

Accepted Answer

Bimodal

Question 16

Which of the following best describes the five-number summary?

Accepted Answer

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

Question 17

A mixture contains 1 lb of raisins at $$1.25/lb$$, 2 lbs of peanuts at $$3.25/lb$$, and 1.5 lbs of cashews at $$5.40/lb. $$What is the weighted mean price per pound?

Accepted Answer

$$\frac{1(1.25) + 2(3.25) + 1.5(5.40)}{4.5} = 3.52$$

Question 18

Which of the following is true about the relationship between mean and median in a symmetric distribution?

Accepted Answer

Mean is roughly equal to median.

Question 19

Which measure of dispersion is least affected by outliers?

Accepted Answer

Interquartile range (IQR)

Numerically Summarizing Data: Measures of Central Tendency, Dispersion, and Position

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