Question 1

Which of the following best describes a bell-shaped distribution in statistics?

Accepted Answer

A distribution with a single pile of values in the middle and tails to the right and left that are approximately mirror images.

Question 2

Which visual display is most useful for identifying the shape of a distribution, such as whether it is bell-shaped, skewed, or symmetric?

Accepted Answer

Histogram

Question 3

Suppose the mean pulse rate in a sample is 70 bpm with a standard deviation of 10 bpm. According to the 95% rule, approximately what interval contains the middle 95% of pulse rates?

Accepted Answer

$$[50, 90]$$

Question 4

A dataset of car braking distances is summarized with a boxplot. Five cars are marked as asterisks far below the rest of the data. What does this indicate?

Accepted Answer

These cars are outliers with unusually short braking distances.

Question 5

Which measure of center is most appropriate to use when a dataset is strongly skewed or contains outliers?

Accepted Answer

Median

Question 6

Given a dataset with a mean of $$\mu = 100$$ and a standard deviation of $$\sigma = 15$$, what is the Z-score for a value $$x = 130$$?

Accepted Answer

$$Z = \frac{130 - 100}{15} = 2$$

Question 7

Which of the following statements about standard deviation is TRUE?

Accepted Answer

Standard deviation is zero only if all values are equal.

Question 8

A histogram of birth rates in all countries shows most values piled up on the left with a long tail to the right. How would you describe the shape of this distribution?

Accepted Answer

Skewed to the right

Question 9

Which of the following is NOT a resistant statistic?

Accepted Answer

Mean

Question 10

If a value in a bell-shaped distribution has a Z-score of 2.5, what can you conclude?

Accepted Answer

The value is unusually high.

Question 11

Which of the following best describes the range of a dataset?

Accepted Answer

The difference between the maximum and minimum values.

Question 12

A distribution is described as symmetric but not bell-shaped. Which of the following could be an example?

Accepted Answer

A histogram with two distinct peaks of equal height.

Question 13

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\Sigma x}{n}$$

Question 14

Which of the following is TRUE about boxplots?

Accepted Answer

Boxplots show the median but not the mean.

Question 15

If the range of temperatures in a city on a given day is $$42.3^{\circ}F$, what does this tell you?

Accepted Answer

The difference between the highest and lowest temperature is $$42.3^{\circ}F$.

Question 16

Which of the following is the correct formula for the Z-score of a value $$x in a $$sample with mean $$\bar{x}$$ and standard deviation $$s$$?

Accepted Answer

$$Z = \frac{x - \bar{x}}{s}$$

Describing and Summarizing One Quantitative Variable

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