Question 1

A business analyst is comparing the annual sales figures of two companies. Company A's sales are distributed symmetrically with no outliers, while Company B's sales are heavily skewed with several outliers. Which summary statistics should the analyst use for each company?

Accepted Answer

Mean and standard deviation for Company A; median and IQR for Company B.

Question 2

Which of the following best describes a histogram?

Accepted Answer

A graphical representation that divides quantitative data into bins and shows the frequency of observations in each bin.

Question 3

A dataset of monthly profits for a company is summarized as follows: mean = $$50,000$$, standard deviation = $$8,000. In $$one month, the company earned $$66,000. $$What is the z-score for this month?

Accepted Answer

$$z = \frac{66,000 - 50,000}{8,000} = 2$$

Question 4

Which measure of center is most resistant to outliers in a dataset?

Accepted Answer

Median

Question 5

A histogram of employee salaries at a tech company shows one main peak and a long tail to the right. How would you describe the shape of this distribution?

Accepted Answer

Unimodal and right-skewed

Question 6

If a dataset has a minimum value of $$10$$ and a maximum value of $$90$$, what is the range?

Accepted Answer

$$80$$

Question 7

A company tracks the number of products sold each day for a month. The data is grouped into bins of 10 units for a histogram. What does the height of each bar represent?

Accepted Answer

The number of days products were sold in that bin range.

Question 8

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

Accepted Answer

IQR measures the spread of the middle 50% of the data.

Question 9

A relative frequency histogram is most useful when:

Accepted Answer

Comparing datasets of different sizes.

Question 10

A dataset of home prices has a mean of $$300,000$$ and a standard deviation of $$50,000. A $$particular home is priced at $$400,000. $$What is the z-score for this home?

Accepted Answer

$$z = \frac{400,000 - 300,000}{50,000} = 2$$

Question 11

Which scenario best illustrates the use of standardizing variables with z-scores?

Accepted Answer

Comparing a company's profit margin to its industry average, and a company's employee satisfaction score to its industry average, to see which is more unusual.

Question 12

If a distribution is uniform, which of the following is true?

Accepted Answer

All bars in the histogram are approximately the same height.

Question 13

A dataset has the following values: $$2, 4, 6, 8, 100. $$Which value is an outlier?

Accepted Answer

$$100$$

Question 14

Which of the following is NOT a correct pairing for summary statistics?

Accepted Answer

Mean and interquartile range (IQR)

Question 15

A distribution of exam scores is bimodal. What does this indicate?

Accepted Answer

There are two main peaks in the distribution.

Question 16

A company wants to compare the performance of two employees. Employee A has a z-score of $$1.5$$ for sales, and Employee B has a z-score of $$-0.5$$ for sales. What does this mean?

Accepted Answer

Employee A's sales are 1.5 standard deviations above the mean; Employee B's sales are 0.5 standard deviations below the mean.

Question 17

Which measure of spread is most appropriate for a symmetric distribution with no outliers?

Accepted Answer

Standard deviation

Question 18

A dataset of daily temperatures is skewed to the left. Which measure of center should be used?

Accepted Answer

Median

Question 19

Which of the following best describes an outlier?

Accepted Answer

A value that is much higher or lower than the rest of the data.

Question 20

A company’s quarterly profits are: $$20,000$$, $$22,000$$, $$21,000$$, $$23,000$$, $$100,000. $$Which measure of center would best represent the typical profit?

Accepted Answer

Median

Displaying and Describing Quantitative Data: Study Notes for Business Statistics

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