Q: Which formula is used to calculate the coefficient of variation for a sample?

$$CV = \frac{s}{\bar{x}} \times 100$$

Q: If a stock has an average price of $$100 and a standard deviation of 5$$, what is its coefficient of variation?

$$CV = \frac{5}{100} \times 100 = 5\%$$

Question 1

Which of the following statements best describes the difference between a statistic and a parameter?

Accepted Answer

A statistic is calculated from sample data, while a parameter is calculated from population data.

Question 2

A business analyst is comparing the mean and median home prices in a city. The mean is much higher than the median. What does this most likely indicate about the distribution of home prices?

Accepted Answer

The distribution is right-skewed.

Question 3

Given the following sample data: 6.2, 7.1, 4.8, 9.0, 3.3, calculate the sample mean using the formula $$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}.$$

Accepted Answer

$$\bar{x} = \frac{30.4}{5} = 6.08$$

Question 4

Which measure of central tendency is most appropriate for describing categorical data?

Accepted Answer

Mode

Question 5

A student earned 9 credit hours of A (4 points), 15 credit hours of B (3 points), 33 credit hours of C (2 points), and 3 credit hours of D (1 point). What is the weighted mean GPA? Use $$\bar{x} = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}.$$

Accepted Answer

$$\bar{x} = \frac{150}{60} = 2.5$$

Question 6

Why is the median often used instead of the mean when reporting home prices in cities like Tampa or Los Angeles?

Accepted Answer

The median is not sensitive to outliers, unlike the mean.

Question 7

Which formula would you use to calculate the sample variance for a data set?

Accepted Answer

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

Question 8

A river has an average depth of 4 feet, but the standard deviation is 3.55 feet. What does this tell you about the river's depth?

Accepted Answer

The river's depth varies greatly, so the average is misleading.

Question 9

Which formula is used to calculate the coefficient of variation for a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} 	imes 100$$

Question 10

If a stock has an average price of $$100 and a standard deviation of 5$$, what is its coefficient of variation?

Accepted Answer

$$CV = \frac{5}{100} 	imes 100 = 5\%$$

Question 11

What does a z-score of -2.5 indicate about a data value in a distribution?

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 12

According to the empirical rule, what percentage of values in a normal distribution fall within ±2 standard deviations of the mean?

Accepted Answer

95%

Question 13

Which formula is used to calculate the percentile position for the pth percentile in a data set of n values?

Accepted Answer

$$i = \frac{p 	imes n}{100}$$

Question 14

A data set has Q1 = 13, Q3 = 22. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 9$$

Question 15

Which formula would you use to determine if a value is an outlier based on quartiles?

Accepted Answer

Upper Limit = $$Q3 + 1.5 	imes IQR$$, Lower Limit = $$Q1 - 1.5 	imes IQR$$

Question 16

Which formula is used to calculate the sample correlation coefficient between two variables x and y?

Accepted Answer

$$r_{xy} = \frac{s_{xy}}{s_x s_y}$$

Question 17

A car dealer finds a correlation coefficient of $$r = 0.95$$ between number of sales representatives and cars sold. What does this indicate?

Accepted Answer

There is a strong positive linear relationship.

Descriptive Statistics: Measures of Central Tendency, Variability, and Association

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