Q: A manufacturer buys 100 pounds at $$4.20 per pound, 300 pounds at 3.80$$, and 100 pounds at $4.50. What is the weighted mean price per pound?

Weighted mean = $$ \frac{100 \times 4.20 + 300 \times 3.80 + 100 \times 4.50}{100 + 300 + 100} $$ = $$3.98$$

Question 1

A compensation analyst is studying a right-skewed salary distribution. Which measure of center and spread should they use to best summarize the data, and why?

Accepted Answer

Median and interquartile range (IQR), because they resist the influence of outliers.

Question 2

A retailer adds $10 to every recorded transaction. What happens to the mean and standard deviation of the transaction amounts?

Accepted Answer

The mean increases by $10, and the standard deviation remains unchanged.

Question 3

A plant converts every defect measurement from centimeters to millimeters by multiplying by 10. What happens to the standard deviation?

Accepted Answer

The standard deviation is multiplied by 10.

Question 4

A bank sends surveys to 3,000 customers, but only 9% reply. What is the leading concern with the results?

Accepted Answer

Nonresponse bias

Question 5

A city surveys transit satisfaction only through its smartphone app. What is the most likely source of bias?

Accepted Answer

Undercoverage bias

Question 6

A manufacturer buys 100 pounds at $$4.20 per pound, 300 pounds at 3.80$$, and 100 pounds at $4.50. What is the weighted mean price per pound?

Accepted Answer

Weighted mean = $$ \frac{100 	imes 4.20 + 300 	imes 3.80 + 100 	imes 4.50}{100 + 300 + 100} $$ = $$3.98$$

Question 7

A distribution of weekly operating profit has mean $$30,000 and standard deviation 5$$,000. Using Chebyshev's theorem, what is the minimum guaranteed percentage of data within three standard deviations of the mean?

Accepted Answer

At least $$1 - \frac{1}{3^2$} = 1 - \frac{1}{9} = 0.8889 or 88.89$$%

Question 8

For approximately bell-shaped data, what percentage of values lie within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

About 95%

Question 9

A sales representative is at the 80th percentile for quarterly revenue. What does this mean?

Accepted Answer

The representative earned more than 80% of the other sales representatives.

Question 10

A result with $$z = -1.4$$ means:

Accepted Answer

1.4 standard deviations below the mean

Question 11

A bank randomly selects six branches and reviews every new account in them. What sampling method is this?

Accepted Answer

Cluster sampling

Question 12

A questionnaire calls a proposed fee increase 'small and necessary.' What type of bias does this wording introduce?

Accepted Answer

Wording-effect bias

Question 13

Annual revenue measured in dollars is usually classified as:

Accepted Answer

Quantitative ratio

Question 14

A constant annual rate that reproduces compounded growth requires which mean?

Accepted Answer

Geometric mean

Question 15

A scatterplot shows a strong negative linear relationship between defect rate and customer rating. What is the likely correlation coefficient?

Accepted Answer

$$r = -0.91$$

Question 16

A hospital compares clinics that chose to adopt a scheduling tool with clinics that did not. What type of study is this, and can it support a causal claim?

Accepted Answer

Observational study; cannot support a causal claim.

Question 17

A result with a coefficient of variation (CV) of 25% for annual administrative expenses means:

Accepted Answer

The standard deviation is 25% of the mean, indicating moderate relative variability.

Question 18

A city wants to compare the percentage composition of three rating categories across divisions of very different sizes. Which display should they use?

Accepted Answer

100% stacked bar chart

Question 19

A survey of remote-work needs excludes employees without company email. What is the main error or bias?

Accepted Answer

Undercoverage bias

Question 20

A scatterplot of training-quality score and retention shows a moderate positive linear relationship. What is the likely sign of covariance?

Accepted Answer

Positive

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