Question 1

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

Accepted Answer

Mean

Question 2

Given the following data set: 2, 4, 4, 6, 8, 10, what is the mode?

Accepted Answer

4

Question 3

A company tracks the monthly sales of two products. Product A has a mean of $$1000 and a standard deviation of 100. $$Product B has a mean of $$500 and a standard deviation of 50. $$Which product has a higher coefficient of variation?

Accepted Answer

Both have the same coefficient of variation

Question 4

What is the formula for the sample variance $$s^2$$ for a sample of size $$n$$ with observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 5

If a distribution is positively skewed, which of the following is the correct order of mean, median, and mode?

Accepted Answer

Mean \u003e Median \u003e Mode

Question 6

A student scored 85 on a test where the mean score was 75 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85-75}{5} = 2$$

Question 7

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third and first quartiles

Question 8

According to Chebyshev's Theorem, what is the minimum percentage of data values that fall within 2 standard deviations of the mean for any distribution?

Accepted Answer

75%

Question 9

Which of the following is NOT a component of the five-number summary?

Accepted Answer

Mean

Question 10

A box-and-whisker plot is constructed using which of the following values?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 11

If the mean and median of a data set are equal, what can be inferred about the shape of the distribution?

Accepted Answer

The distribution is symmetric

Question 12

Which measure is most appropriate for comparing the variability of two data sets with different units?

Accepted Answer

Coefficient of variation

Question 13

What is the formula for the population mean $$\mu$$ for $$N$$ values $$x_1$$, $$x_2$$, ..., x_N$$?

Accepted Answer

$$\mu = \frac{\sum_{i=1}^N x_i}{N}$$

Question 14

A dataset has a mean of 50 and a standard deviation of 10. According to the empirical rule, approximately what percentage of data falls between 40 and 60?

Accepted Answer

68%

Question 15

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ ranges from -1 to 1

Question 16

If the covariance between two variables X and Y is negative, what does this indicate?

Accepted Answer

X and Y tend to move in opposite directions

Question 17

Which formula is used to find the position of the median in an ordered data set of size $$n$$?

Accepted Answer

$$\frac{n+1}{2}$$

Question 18

A weighted mean is most useful when:

Accepted Answer

Data is grouped into classes with different frequencies

Question 19

Which of the following is a disadvantage of using the range as a measure of variability?

Accepted Answer

It ignores the way data are distributed

Question 20

If a dataset is divided into four equal parts, what are the boundaries called?

Accepted Answer

Quartiles

Describing Data: Numerical Measures – Study Notes for Statistics for Business

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