Q: A data set has Q1 = 20, Q3 = 40. What is the upper limit for outliers?

$$Q3 + 1.5 \times (Q3 - Q1) = 40 + 1.5 \times 20 = 70$$

Q: A sample has a mean of 100 and a standard deviation of 20. What is the coefficient of variation (CV)?

$$CV = \frac{20}{100} \times 100 = 20\%$$

Question 1

A company has five machines producing widgets. The number of widgets produced in a day by each machine is: 250, 300, 350, 400, and 13500. What is the sample mean of widgets produced per machine?

Accepted Answer

$$\frac{250 + 300 + 350 + 400 + 13500}{5} = 2880$$

Question 2

Refer to the histogram showing the distribution of steel plate thicknesses. If the mean is 55 and the standard deviation is 15.7, what percentage of plates are expected to fall within the range 39.3 to 70.7 mm according to the Empirical Rule?

Accepted Answer

Approximately 68%

Question 3

A histogram of steel plate thicknesses is shown with the mean shifted to 45 and the standard deviation unchanged at 15.7. What is the main implication for quality control?

Accepted Answer

The proportion of conforming plates decreases.

Question 4

Given a perfectly uniform histogram where all values are 50-60 mm, what are the mean and standard deviation?

Accepted Answer

Mean = 55, Standard deviation = 0

Question 5

In Excel, which function would you use to calculate the sample standard deviation for a data set in cells A2:A6?

Accepted Answer

=STDEV.S(A2:A6)

Question 6

A data set of house prices is highly right-skewed due to one very expensive house. Which measure of central tendency best describes the typical house price?

Accepted Answer

Median

Question 7

Given the following five-number summary for national park visitors (in millions): Min = 0.39, Q1 = 1.39, Median = 2.71, Q3 = 3.45, Max = 9.69. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 3.45 - 1.39 = 2.06$$

Question 8

Using the boxplot for national park visitors, which value is considered an outlier?

Accepted Answer

9.69

Question 9

A music download site records the number of downloads per hour for 24 hours. The histogram is unimodal and roughly symmetric. Which measure(s) of central tendency are most appropriate to describe the data?

Accepted Answer

Both mean and median

Question 10

A histogram of store sales is highly right-skewed with several high outliers. Which measure of spread is most appropriate to summarize the variability in sales?

Accepted Answer

Interquartile range (IQR)

Question 11

Given the summary statistics for food store sales: Mean = $$107,844.94, Median = 95$$,974.50, Std Dev = $$46,962.19, IQR = 43$$,300. What would happen to the mean and standard deviation if the two highest outliers were removed?

Accepted Answer

Mean would decrease, standard deviation would decrease.

Question 12

A boxplot of ozone levels by month shows the largest IQR in February and the smallest range in August. What does this indicate about the variability of ozone levels?

Accepted Answer

Ozone levels are most variable in February and least variable in August.

Question 13

If a distribution is left-skewed, which of the following is most likely true?

Accepted Answer

Mean \u003c Median

Question 14

Which Excel function would you use to find the 75th percentile of a data set in cells A2:A20?

Accepted Answer

=QUARTILE.EXC(A2:A20, 3)

Question 15

A data set has Q1 = 20, Q3 = 40. What is the upper limit for outliers?

Accepted Answer

$$Q3 + 1.5 	imes (Q3 - Q1) = 40 + 1.5 	imes 20 = 70$$

Question 16

If a value in a data set has a z-score of 2.5, what does this mean?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Question 17

Which of the following is NOT a property of the median?

Accepted Answer

It is affected by outliers.

Question 18

A sample has a mean of 100 and a standard deviation of 20. What is the coefficient of variation (CV)?

Accepted Answer

$$CV = \frac{20}{100} 	imes 100 = 20\%$$

Question 19

Which of the following best describes a bimodal distribution?

Accepted Answer

It has two peaks.

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

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