1.6 Descriptions for One Quantitative Variable Distributions

Describe distributions of quantitative one-variable graphical representations.

• Descriptions of the distribution of one quantitative variable include shape, center, and variability (spread) as well as any unusual features such as outliers, gaps, or clusters in context.
• The shape of the distribution of one quantitative variable is skewed to the right (positively skewed) if the right tail (toward larger values) is longer than the left. The shape of the distribution is skewed to the left (negatively skewed) if the left tail (toward smaller values) is longer than the right. The shape of the distribution is approximately symmetric if the left half is approximately the mirror image of the right half.
• Distributions of one quantitative variable with one main peak are called unimodal. Distributions with two prominent peaks are called bimodal. A distribution in which each frequency or each relative frequency is approximately the same with no prominent peaks is approximately uniform.
• Outliers for one quantitative variable are data points that are unusually small or large relative to the rest of the data.
• A gap is a region in a distribution between two values in which there are no observed data.
• Clusters are concentrations of values usually separated by gaps.

Justify a claim using distributions of quantitative one-variable graphical representations.

• Graphical representations of a quantitative variable may reveal information that can be used to justify claims about the variable in context.