Question 1

Which of the following statements best describes the arithmetic mean?

Accepted Answer

It is the sum of all values divided by the number of values.

Question 2

A sample of exam scores is: 70, 75, 80, 85, 90. What is the median score?

Accepted Answer

$$80$$

Question 3

Which measure of central tendency is least affected by extreme values (outliers)?

Accepted Answer

Median

Question 4

Given the data set: 2, 4, 4, 4, 5, 7, 9, what is the mode?

Accepted Answer

$$4$$

Question 5

Which formula correctly represents the sample variance?

Accepted Answer

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

Question 6

A company tracks the monthly sales (in thousands): 20, 22, 25, 30, 35. What is the range?

Accepted Answer

$$15$$

Question 7

Which of the following is always true about the standard deviation?

Accepted Answer

It is always zero or positive.

Question 8

If a distribution is right-skewed, which of the following is true?

Accepted Answer

Median \u003c Mean

Question 9

A sample has a mean of $$50$$ and a standard deviation of $$5. $$What is the Z-score for a value of $$60$$?

Accepted Answer

$$\frac{60-50}{5} = 2$$

Question 10

Which of the following best describes the coefficient of variation?

Accepted Answer

It is the ratio of the standard deviation to the mean, expressed as a percentage.

Question 11

The five-number summary includes which of the following?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 12

Which formula is used to calculate the Z-score for a data value $$X in a $$sample?

Accepted Answer

$$Z = \frac{X - \bar{X}}{s}$$

Question 13

Which of the following is NOT a resistant measure (not robust to outliers)?

Accepted Answer

Mean

Question 14

A boxplot is most useful for which of the following?

Accepted Answer

Showing the five-number summary and identifying outliers

Question 15

Which formula represents the sample covariance between variables $$X$$ and $$Y$$?

Accepted Answer

$$\frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{n-1}$$

Question 16

If the coefficient of correlation $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

A strong negative linear relationship

Question 17

Which of the following is true about the empirical rule for a normal distribution?

Accepted Answer

About 68% of data falls within one standard deviation of the mean.

Question 18

A distribution has a mean of $$100$$, a median of $$80$$, and a mode of $$60. $$What is the likely shape of the distribution?

Accepted Answer

Right-skewed

Question 19

Which of the following is a population parameter, not a sample statistic?

Accepted Answer

$$\mu ($$population mean)

Question 20

Which of the following is NOT included in the five-number summary?

Accepted Answer

Mean

Numerical Descriptive Measures in Business Statistics

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