Describing Data

Open Ended

Why is it important to understand the distribution of data when analyzing information?

Multiple Choice

Which of the following best describes a symmetric distribution?

• The data are evenly distributed.

• The majority of the data are on the right.

• The majority of the data are on the left.

• The data are not distributed at all.

Multiple Choice

What does it mean if a histogram is high on the left and has a tail on the right?

• The distribution is positively skewed.

• The distribution is negatively skewed.

• The distribution is symmetric.

• The distribution is bimodal.

Open Ended

Explain how a box-and-whisker plot can be used to identify the shape of a distribution. Use the data from Example 1 as a reference.

Multiple Choice

Given a box-and-whisker plot where the right whisker is longer than the left and the median is closer to the left, what type of skewness does the distribution have?

• Positively skewed

• Negatively skewed

• Symmetric

• Uniform

Fill in the Blanks

In a negatively skewed box-and-whisker plot, the left whisker is

than the right whisker.

Multiple Select

Which of the following statements are true about a symmetric box-and-whisker plot?

• The whiskers are the same length.

• The median is in the center of the data.

• The left whisker is longer than the right.

• The right whisker is longer than the left.

Open Ended

Describe the steps you would take to use a graphing calculator to construct a box-and-whisker plot for a given data set and determine the shape of its distribution.

Open Ended

Explain why the mean is not a reliable measure of center for a skewed distribution, based on the the pictures.

Multiple Choice

Which statistic is more reliable for describing the center of a skewed distribution: mean or median?

• Mean

• Median

• Both are equally reliable

• Neither

Fill in the Blanks

The mean x̄ is about

with standard deviation σ of about 7.1.

Open Ended

List the five components of the five-number summary used in a box-and-whisker plot.

Multiple Choice

When is it appropriate to use the five-number summary instead of the mean and standard deviation to describe a data set?

• When the distribution is symmetric

• When the distribution is skewed or has outliers

• When the data set is small

• When the mean and median are equal

Multiple Choice

What does it indicate about a data set if the right whisker in a box-and-whisker plot is longer than the left whisker and the median is closer to the left whisker?

• The distribution is symmetric

• The distribution is negatively skewed

• The distribution is positively skewed

• The data set has no outliers

Open Ended

How would you describe the overall shape of a symmetric distribution, and why is it important when analyzing data?

Multiple Choice

What is the main difference between a negatively skewed distribution and a positively skewed distribution?

• In a negatively skewed distribution, the majority of the data are on the right, while in a positively skewed distribution, the majority of the data are on the left.

• In a negatively skewed distribution, the majority of the data are on the left, while in a positively skewed distribution, the majority of the data are on the right.

• Both distributions have the majority of data in the center.

• Both distributions have the majority of data on the right.

Poll

How do you feel about Describing Data?