Question 1

Which of the following best describes the shape of the distribution in the first histogram (Sample Value vs. Frequency)?

Accepted Answer

The distribution is approximately bell-shaped and symmetric.

Question 2

Refer to the second graph (Unemployment Rates). What is the main issue with the way the years are displayed on the horizontal axis?

Accepted Answer

The years are in reverse chronological order, which can mislead the viewer.

Question 3

In the second graph, what additional issue can be identified with the vertical axis?

Accepted Answer

The vertical axis starts at a value greater than zero, exaggerating differences.

Question 4

Suppose you are asked to improve the second graph. Which of the following changes would make the graph more accurate and less misleading?

Accepted Answer

Reverse the order of the years so that time increases from left to right and start the vertical axis at zero.

Question 5

Given the first histogram, what is the modal class?

Accepted Answer

60-65

Question 6

If the mean of the sample values in the first histogram is 64 and the standard deviation is 3, what percentage of the data falls within one standard deviation of the mean according to the Empirical Rule?

Accepted Answer

$$68\%$$

Question 7

A student claims that the first histogram shows a bimodal distribution. Is this claim correct? Why or why not?

Accepted Answer

No, because there is only one clear peak in the distribution.

Question 8

If the maximum sample value in the first histogram is 72 and the minimum is 56, use the Range Rule of Thumb to estimate the standard deviation.

Accepted Answer

$$\frac{72-56}{4} = 4$$

Question 9

Suppose the mean unemployment rate from 1992 to 2001 (second graph) is $$5.5\%$$ with a standard deviation of $$1.2\%. $$What is the z-score for the year 1992 with an unemployment rate of $$7.6\%$$?

Accepted Answer

$$z = \frac{7.6 - 5.5}{1.2} = 1.75$$

Question 10

Which of the following best describes why the second graph could lead to a misinterpretation of unemployment trends?

Accepted Answer

The reversed order of years and non-zero axis exaggerate the increase in unemployment.

Question 11

If you were to construct a cumulative frequency distribution from the first histogram, what would the cumulative frequency be at the class interval 65-70?

Accepted Answer

It would be the sum of all frequencies up to and including the 65-70 class.

Question 12

Which of the following is a valid critique of the first histogram if the class widths are not equal?

Accepted Answer

The histogram may misrepresent the distribution because unequal class widths distort the visual impression.

Statistics Test 1 Study Guide – Step-by-Step Guidance

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