Question 1

A food products firm surveyed 100 consumers to rate a new snack food on a scale from 0 to 15. The mean score was 7.94 and the standard deviation was 3.26. What does the standard deviation tell the managers about the taste-test scores?

Accepted Answer

It tells them the average distance of the scores from the mean, indicating how spread out the ratings are.

Question 2

Given the data set: 4, 5, 14, 9, 7, calculate the sample mean $\bar{x}$ using the formula $\bar{x} = \frac{\sum_{i=1}^n x_i}{n}$.

Accepted Answer

$\bar{x} = 7.8$

Question 3

Which measure of location is most robust to extreme values (outliers) in a data set?

Accepted Answer

Median

Question 4

A data set has the following values: 10, 5, -1, -1, 0, 2, -1, 0, 3, 2, 4, 5. What is the mode of this data set?

Accepted Answer

-1

Question 5

If the mean of a data set is much greater than the median, what can you infer about the shape of the distribution?

Accepted Answer

The distribution is right-skewed (positively skewed).

Question 6

Which formula correctly represents the sample variance $s^2$ for a data set with $n$ observations?

Accepted Answer

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

Question 7

A company wants to summarize the taste-test data for managers who are not familiar with statistics. Which of the following is the most effective way to communicate the results?

Accepted Answer

Report the mean, median, and standard deviation, and show a histogram of the scores.

Question 8

Given the following sample: $2, 3, 1, 4, 5$, calculate the sample variance using the computational formula: $s^2 = \frac{\sum_{i=1}^n x_i^2 - \frac{(\sum_{i=1}^n x_i)^2}{n}}{n-1}$.

Accepted Answer

$s^2 = 2.5$

Question 9

Why is the range considered a poor measure of variability for large data sets?

Accepted Answer

It only considers the two most extreme values and ignores the rest of the data.

Question 10

A taste-test score of 12 has a mean of 7.94 and a standard deviation of 3.26. What is the $z$-score for this observation? Use $z = \frac{x - \bar{x}}{s}$.

Accepted Answer

$z = 1.25$

Question 11

Which of the following statements about the mean and median is correct?

Accepted Answer

The median is more robust to outliers than the mean.

Question 12

If a data set is bimodal, what does this mean?

Accepted Answer

There are two values that occur with the same highest frequency.

Question 13

A manager wants to compare the relative standing of two employees' sales numbers. Which statistic should they use?

Accepted Answer

Z-score

Question 14

Which of the following is NOT a measure of location?

Accepted Answer

Variance

Question 15

A histogram of household incomes is highly right-skewed. Which measure of central tendency would best represent the 'typical' household income?

Accepted Answer

Median

Question 16

If the variance of a data set is $s^2 = 10.62$, what are the units of the variance if the data are measured in dollars?

Accepted Answer

Dollars squared

Question 17

Which of the following best describes an outlier in a box plot?

Accepted Answer

A value that is detached from the rest of the data set.

Question 18

A company is comparing two investments. Stock A has a lower variance in price than Stock B. What does this imply?

Accepted Answer

Stock A's prices are more consistent and less spread out than Stock B's.

Question 19

Which of the following is the correct formula for the population variance $\sigma^2$?

Accepted Answer

$\sigma^2 = \frac{\sum_{i=1}^N (x_i - \mu)^2}{N}$

Question 20

If a data set has a mean of 20 and a standard deviation of 5, what is the $z$-score for a value of 30?

Accepted Answer

$z = 2$

Numerical Descriptive Measures for Business Statistics: Location, Variability, and Relative Standing

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