Q: Which formula is used to calculate the population covariance between variables $$X$$ and $$Y$$? $$\mu_X$$ and $$\mu_Y$$ are the population means.

$$\text{cov}(X,Y) = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu_X)(y_i - \mu_Y)$$

Question 1

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

Accepted Answer

A population parameter is a descriptive measure calculated from the entire population, while a sample statistic is calculated from a sample.

Question 2

Given a data set with the following values: $$[10, 12, 14, 16, 18]$$, what is the sample mean $$\bar{x}$$?

$$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$$

Accepted Answer

$$\bar{x} = 14$$

Question 3

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 4

A company tracks the repair times (in days) for 250 computers. The mean is 14.912, the median is 14, and the mode is 15. What does this suggest about the distribution of repair times?

Accepted Answer

The distribution is likely negatively skewed.

Question 5

Given the following cost per order data: Maximum = $$127,500, Minimum = 68.78. $$What is the range?

Accepted Answer

$$127,431.22$$

Question 6

Which formula correctly calculates the sample variance $$s^2$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 7

If the standard deviation of Intel's stock price is $$0.50$$ and the mean is $$18.81$$, what is the coefficient of variation (CV)?

$$CV = \frac{	ext{Standard Deviation}}{	ext{Mean}}$$

Accepted Answer

$$0.027$$

Question 8

Which of the following statements about the interquartile range (IQR) is correct?

Accepted Answer

IQR is the difference between the third and first quartiles and is not influenced by extreme values.

Question 9

A histogram of a data set shows a long right tail. Which of the following is true about the skewness?

Accepted Answer

The data is positively skewed.

Question 10

Which Excel function would you use to compute the sample standard deviation for a data set in column B?

Accepted Answer

=STDEV.S(B:B)

Question 11

If the coefficient of skewness (CS) for a data set is $$-0.8$$, what does this indicate?

Accepted Answer

The data is moderately negatively skewed.

Question 12

Which of the following best describes the meaning of a correlation coefficient $$r = -0.55$$ between acceptance rate and graduation rate for universities?

Accepted Answer

There is a moderate negative linear relationship; as acceptance rate increases, graduation rate tends to decrease.

Question 13

Which formula is used to calculate the population covariance between variables $$X$$ and $$Y$$?

$$\mu_X$$ and $$\mu_Y$$ are the population means.

Accepted Answer

$$	ext{cov}(X,Y) = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu_X)(y_i - \mu_Y)$$

Question 14

A company wants to summarize the proportion of orders placed by a specific supplier. Which formula should they use if there are 12 such orders out of 94 total orders?

Accepted Answer

$$p = \frac{12}{94}$$

Question 15

Which of the following is NOT a measure of dispersion?

Accepted Answer

Median

Question 16

If a data set has a kurtosis coefficient $$CK \u003c 3$$, what does this indicate about the shape of the distribution?

Accepted Answer

The distribution is flat with a wide degree of dispersion.

Question 17

Which of the following statements about correlation is correct?

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two variables.

Question 18

A data set has a mean of $$20$$ and a standard deviation of $$5. $$What is the coefficient of variation (CV)?

$$CV = \frac{	ext{Standard Deviation}}{	ext{Mean}}$$

Accepted Answer

$$0.25$$

Question 19

Which Excel function would you use to find the most frequently occurring value in a data set?

Accepted Answer

=MODE.SNGL(data range)

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