Question 1

Which of the following best describes a unimodal distribution?

Accepted Answer

A distribution with only one peak.

Question 2

A histogram of household income in a city shows a long tail to the right. What is the shape of this distribution?

Accepted Answer

Right skewed

Question 3

Which of the following is true about a symmetric distribution?

Accepted Answer

It can be divided into two pieces that are mirror images of one another.

Question 4

Suppose you collect the heights of 1000 adult males and plot the histogram. The graph appears bell-shaped and symmetric. Which distribution shape does this most likely represent?

Accepted Answer

Bell shaped

Question 5

Which of the following statements about sample and population distributions is correct?

Accepted Answer

There is only one population distribution for a given variable.

Question 6

A dataset of exam scores has a histogram with a long tail to the left. Which of the following best describes the distribution?

Accepted Answer

Left skewed

Question 7

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

Accepted Answer

All values occur with approximately the same frequency.

Question 8

Which of the following best describes a bimodal distribution?

Accepted Answer

A distribution with two distinct peaks.

Question 9

Why do statisticians often use the distribution of a simple random sample to estimate the population distribution?

Accepted Answer

Because the population distribution is usually unknown.

Question 10

Which of the following statements is true regarding the approximation of the population distribution by the sample distribution?

Accepted Answer

The larger the sample size, the better the approximation.

Question 11

A researcher draws six samples of 100 households each from the U.S. population and plots the distribution of household sizes for each sample. What is the most likely observation?

Accepted Answer

Sample distributions will vary from sample to sample.

Question 12

Which of the following is NOT a characteristic of a right-skewed distribution?

Accepted Answer

The left tail is longer than the right tail.

Question 13

Given a histogram of the number of people per household that shows most households have 1 or 2 people and fewer households have 5 or more, what is the likely shape of the distribution?

Accepted Answer

Right skewed

Question 14

Which of the following best describes the difference between population distribution and sample distribution?

Accepted Answer

Population distribution refers to the distribution of the variable in the entire population, while sample distribution refers to the distribution in a specific sample.

Question 15

A dataset of reaction times in a psychological experiment shows two distinct peaks. Which term best describes this distribution?

Accepted Answer

Bimodal

Question 16

Which of the following is a real-world example of a left-skewed distribution?

Accepted Answer

Distribution of ages at retirement (most retire at older ages, few at younger ages)

Question 17

If a distribution is described as multimodal, what does this mean?

Accepted Answer

It has three or more peaks.

Question 18

Which formula would you use to calculate the relative frequency of a value in a dataset?

Accepted Answer

$$ \frac{	ext{Number of times the value occurs}}{	ext{Total number of observations}} $$

Question 19

A sample distribution is used to estimate the population distribution. Which of the following strategies improves the accuracy of this estimation?

Accepted Answer

Increasing the sample size.

Question 20

Which of the following is most likely to be symmetric?

Accepted Answer

Distribution of heights in adult males.

Distribution Shapes in Statistics: Concepts and Applications

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