Q: A business wants to compare the consistency of two products. Product A has a mean of 100 and a standard deviation of 8. Product B has a mean of 200 and a standard deviation of 12. Which product is more consistent based on the coefficient of variation?

Product A: $$CV = \frac{8}{100} \times 100 = 8\%$$, Product B: $$CV = \frac{12}{200} \times 100 = 6\%. $$Product B is more consistent.

Q: Given a data set with $$Q_1 = 15$, Q_3$ = 35$$, and $$IQR = 20$$, what is the upper limit for outliers?

$$Upper\ Limit = Q_3$ + 1.5 \times IQR = 35 + 1.5 \times 20 = 65$$

Q: A student scored 82 on a statistics exam. The class scores are: 66, 69, 70, 72, 73, 76, 78, 78, 79, 79, 80, 80, 81, 84, 84, 85, 86, 87, 88, 89, 89, 92, 96, 99, 100. What is the percentile rank of 82?

$$(13 + 0.5)/25 \times 100 = 54\%$$

Question 1

A company has five employees with the following annual salaries (in $): 25,000; 27,000; 30,000; 35,000; 135,000. Calculate the sample variance for these salaries.

Accepted Answer

$$\frac{135000^2$ + 35000^2$ + 30000^2$ + 27000^2$ + 25000^2$ - \frac{(252000)^2$}{5}}{4} = 1350000000$$

Question 2

Which measure of central tendency is most appropriate to describe the center of a data set with significant outliers?

Accepted Answer

Median

Question 3

A sample of 8 airline flights had the following arrival times (in minutes): 14, -17, 31, -10, 0, 11, 5, 18. What is the sample mean?

Accepted Answer

$$\frac{14 + (-17) + 31 + (-10) + 0 + 11 + 5 + 18}{8} = 6.5$$

Question 4

Given a data set with a mean of 50 and a standard deviation of 20, what is the z-score for a value of 70?

Accepted Answer

$$z = \frac{70 - 50}{20} = 1$$

Question 5

A business wants to compare the consistency of two products. Product A has a mean of 100 and a standard deviation of 8. Product B has a mean of 200 and a standard deviation of 12. Which product is more consistent based on the coefficient of variation?

Accepted Answer

Product A: $$CV = \frac{8}{100} 	imes 100 = 8\%$$, Product B: $$CV = \frac{12}{200} 	imes 100 = 6\%. $$Product B is more consistent.

Question 6

If a distribution is left-skewed, which of the following is true about the relationship between the mean and the median?

Accepted Answer

Mean \u003c Median

Question 7

A sample of 7 adults read the following number of books last year: 10, 10, 4, 8, 13, 6, 11. What is the sample variance?

Accepted Answer

$$s^2$$ = \frac{606 - \frac{$$62^2$$}{7}}{6} = 9.48$$

Question 8

Which of the following best describes the Empirical Rule for a bell-shaped distribution?

Accepted Answer

About 68% of data falls within $$\pm 1$$ standard deviation, 95% within $$\pm 2$$, and 99.7% within $$\pm 3$$ standard deviations from the mean.

Question 9

A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 40 - 20 = 20$$

Question 10

Given a data set with $$Q_1 = 15$, Q_3$ = 35$$, and $$IQR = 20$$, what is the upper limit for outliers?

Accepted Answer

$$Upper\ Limit = Q_3$ + 1.5 	imes IQR = 35 + 1.5 	imes 20 = 65$$

Question 11

A student scored 82 on a statistics exam. The class scores are: 66, 69, 70, 72, 73, 76, 78, 78, 79, 79, 80, 80, 81, 84, 84, 85, 86, 87, 88, 89, 89, 92, 96, 99, 100. What is the percentile rank of 82?

Accepted Answer

$$(13 + 0.5)/25 	imes 100 = 54\%$$

Question 12

If the mean price of homes in a neighborhood is $$50,000 with a standard deviation of 10$$,000, what is the price range that includes at least 75% of the homes according to Chebyshev’s Theorem?

Accepted Answer

$$\30$$,000$$ to $$\$$70,000$$

Question 13

Which Excel function would you use to calculate the sample standard deviation for a data set in column A from row 2 to row 10?

Accepted Answer

=STDEV.S(A2:A10)

Question 14

A boxplot shows the median closer to the lower quartile and the right whisker is longer than the left. What does this indicate about the distribution?

Accepted Answer

The distribution is positively (right) skewed.

Question 15

A frequency distribution of steel plate thicknesses is centered at 55 mm with a standard deviation of 15.7 mm. If the mean shifts to 65 mm but the standard deviation remains unchanged, what happens to the proportion of plates conforming to the 50-60 mm specification?

Accepted Answer

The proportion of conforming plates decreases.

Question 16

Which of the following is NOT a limitation of the range as a measure of variability?

Accepted Answer

It uses all data points in its calculation.

Question 17

A data set has the following values: 10, 20, 30, 40, 50. What is the median?

Accepted Answer

30

Descriptive Statistics: Measures of Central Tendency, Variation, and Relative Position

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