Q: A company wants to compare the consistency of two products’ weights. Product A has a mean weight of 100g and a standard deviation of 2g. Product B has a mean weight of 50g and a standard deviation of 1.5g. Which product is more consistent based on the coefficient of variation?

Product A, because $$CV = \frac{2}{100} \times 100 = 2\% is $$lower than Product B’s $$CV = 3\%.$$

Q: A box-and-whisker plot is constructed for a data set. If a value is plotted as an asterisk beyond the right whisker, what does this indicate?

The value is an outlier, greater than $$Q3 + 1.5 \times IQR.$$

Question 1

Which of the following statements best describes the main disadvantage of using the mean as a measure of central tendency in a business context?

Accepted Answer

The mean can be heavily influenced by outliers, which may not represent the typical value in the data set.

Question 2

A company tracks the number of products sold each day for a week: 12, 15, 13, 14, 100, 13, 14. Which measure of central tendency would best represent the typical daily sales, and why?

Accepted Answer

The median, because it is not affected by the outlier (100) and better represents the center of the data.

Question 3

Given the following data set representing the number of sales per day: 5, 7, 7, 8, 10, 12, 12, 12, 15. What is the mode?

Accepted Answer

12

Question 4

Which formula correctly represents the sample mean $$\bar{x}$$ for a data set with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 5

A student’s final grade is based on three components: Exam (94, weight 50%), Project (92, weight 35%), and Homework (100, weight 15%). What is the weighted mean of the student’s scores?

Accepted Answer

94.2

Question 6

Which of the following is NOT an advantage of using the median as a measure of central tendency?

Accepted Answer

It can be used with categorical data.

Question 7

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

$$z = 2$$

Question 8

Which formula is used to calculate the sample variance $$s^2$$ for a data set with $$n$$ values?

Accepted Answer

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

Question 9

A company wants to compare the consistency of two products’ weights. Product A has a mean weight of 100g and a standard deviation of 2g. Product B has a mean weight of 50g and a standard deviation of 1.5g. Which product is more consistent based on the coefficient of variation?

Accepted Answer

Product A, because $$CV = \frac{2}{100} 	imes 100 = 2\% is $$lower than Product B’s $$CV = 3\%.$$

Question 10

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

Accepted Answer

95%

Question 11

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

Accepted Answer

The difference between the third quartile (Q3) and the first quartile (Q1).

Question 12

A box-and-whisker plot is constructed for a data set. If a value is plotted as an asterisk beyond the right whisker, what does this indicate?

Accepted Answer

The value is an outlier, greater than $$Q3 + 1.5 	imes IQR.$$

Question 13

Which formula is used to calculate the sample correlation coefficient $$r_{xy}$$ between two variables $$x$$ and $$y$$?

Accepted Answer

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

Question 14

If the sample correlation coefficient $$r$$ between hours studied and exam grade is 0.95, what does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam grade.

Question 15

A data set of 100 values is grouped into 5 classes. To estimate the mean from the grouped data, which formula should be used?

Accepted Answer

$$\bar{x}_g = \frac{\sum\limits_{i=1}^{k} f_i m_i}{n}$$

Question 16

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

Accepted Answer

=STDEV.S(A:A)

Question 17

A value in a data set has a z-score of -2.5. What does this indicate about the value?

Accepted Answer

It is 2.5 standard deviations below the mean.

Question 18

Chebyshev’s Theorem states that for any distribution, at least what percentage of values fall within 2 standard deviations of the mean?

Accepted Answer

75%

Descriptive Statistics: Measures of Central Tendency and Variability

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