Summarize Distributions

This is a skewed right distribution

• True

• False

Answer explanation

A skewed right distribution has a longer tail on the right side, indicating that most values are concentrated on the left. Therefore, the statement is true.

Which of the following statements are correct based on the data shown? Select all correct answers.

• This is a normal distribution.

• This is a uniform distribution

• The mean and median are equal

• The median is less than the mean.

Answer explanation

The data represents a normal distribution, where the mean and median are equal. This confirms the correct choices: 'This is a normal distribution' and 'The mean and median are equal'. The other statements are incorrect.

Which of the following statements are correct based on the data shown? Select all correct answers.

• This is a skewed left distribution.

• This is a uniform distribution

• The mean and median are about the same

• The median is less than the mean.

Answer explanation

In a left-skewed distribution, the mean is typically greater than the median. Therefore, the statement 'The median is less than the mean' is correct, indicating the distribution is skewed left.

This is a uniform distribution

• True

• False

Answer explanation

The statement is false because a uniform distribution implies that all outcomes are equally likely, which is not specified in the question. Therefore, it cannot be assumed to be a uniform distribution.

Which of the following statements is true?

• The median is greater than the mean

• This is a skewed right distribution

• Most values are less than 4

• The median and the mean are the same

Answer explanation

In a skewed right distribution, the mean is typically greater than the median. Therefore, the statement 'The median is greater than the mean' is true, indicating that the distribution has a longer tail on the right.

This is a uniform distribution

• True

• False

Answer explanation

The statement indicates that the distribution is uniform, meaning all outcomes are equally likely. Therefore, the correct answer is True.

The IQR is a better measure of variability than the range for this distribution

• True

• False

Answer explanation

True. The IQR (Interquartile Range) measures the middle 50% of data, making it less sensitive to outliers than the range, which considers the entire dataset. Thus, IQR provides a more robust measure of variability.

The median is the better measure of center for this distribution

• True

• False

Answer explanation

The median is less affected by outliers and skewed data than the mean, making it a better measure of center for distributions that are not symmetrical. Therefore, the statement is true.

Which of the following distributions is most likely to have a mean that is less than the median?

• Skewed left distribution

• Skewed right distribution

• Uniform distribution

• Normal distribution

Answer explanation

A skewed left distribution has a longer tail on the left side, pulling the mean down below the median. In contrast, skewed right, uniform, and normal distributions typically have the mean greater than or equal to the median.

This distribution is....

• skewed left

• skewed right

• uniform

• normal