Question 1

Refer to the histogram of hourly wages of employees (Image 1). Which of the following best describes the shape of the distribution?

Accepted Answer

Skewed right

Question 2

In the hourly wage histogram (Image 1), points A, B, and C are marked on the horizontal axis. If A, B, and C represent the mode, median, and mean, respectively, which point corresponds to the mean?

Accepted Answer

C

Question 3

Which of the following histograms (Images 2, 3, 4) represents a data set with the largest standard deviation?

Accepted Answer

Image 4

Question 4

Which histogram (Images 2, 3, 4) represents a uniform distribution?

Accepted Answer

Image 4

Question 5

Refer to the bell-shaped distribution (Image 5). According to the Empirical Rule, what percentage of data falls within two standard deviations of the mean?

Accepted Answer

$$95\%$$

Question 6

Using the bell-shaped distribution (Image 5), between which values does approximately $$68\% of $$the data lie?

Accepted Answer

$$\bar{x} \pm s$$

Question 7

Refer to the population distributions for Georgia and Iowa (Images 6 and 7). If $$\mu_{GA} = 38.2$$ and $$\sigma_{GA} = 22.6$$, use Chebyshev’s Theorem with $$k=2 to $$estimate the minimum percentage of Georgia residents with ages between $$\mu - 2\sigma$$ and $$\mu + 2\sigma.$$

Accepted Answer

$$75\%$$

Question 8

Based on the Georgia and Iowa age distributions (Images 6 and 7), is an age of 90 considered unusual for either state? Use the mean and standard deviation provided.

Accepted Answer

Yes, because 90 is more than two standard deviations above the mean for both states.

Question 9

Refer to the ogive (Image 8). What score represents the 50th percentile?

Accepted Answer

About 155

Question 10

Using the ogive (Image 8), what percentile corresponds to a score of 162?

Accepted Answer

About the 90th percentile

Question 11

A data set has a mean $$\mu = 4$$ and all values are equal to 4 (Image 2). What is the standard deviation of this data set?

Accepted Answer

$$\sigma = 0$$

Question 12

Which of the following best describes the distribution in Image 3?

Accepted Answer

Symmetric and bimodal

Question 13

If a distribution is bell-shaped and symmetric (Image 5), which measure of central tendency is most appropriate to describe the center?

Accepted Answer

Mean

Question 14

In the hourly wage histogram (Image 1), which measure of central tendency is most affected by the presence of low outliers?

Accepted Answer

Mean

Question 15

Given the bell-shaped distribution (Image 5), what is the probability that a randomly selected value falls more than two standard deviations from the mean?

Accepted Answer

$$100\% - 95\% = 5\%$$ total

Descriptive Statistics: Measures of Central Tendency, Variation, and Position

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