This page would contain resource information like a glossary of terms from the section, key equations, and a reminder of concepts that were covered.
Essential Concepts
- The description of a distribution of a quantitative variable can be identified using the shape, center, spread, and presence of outliers.
- The shape of a distribution has two parts to consider, overall pattern (left-skewed, symmetric, and right-skewed) and the number of peaks (unimodal, bimodal, and multimodal). Uniform is included in the modality, but represents no peaks present in the distribution.
- The center describes the point in the distribution where about half of the observations are below it and half are above it. The use of histograms help you approximate this value.
- When describing the spread of a distribution that is left-skewed, right-skewed, or has outliers, it can be misleading to only rely on the range to measure spread, since it is influenced by skewness and outliers. In this case, the range may make the spread appear to be larger than it is for a vast majority of the data.
Glossary
- minimum
- the smallest observation or value.
- maximum
- the largest observation or value.
- shape
- the overall pattern (left skewed, right skewed, symmetric) and the number of peaks (unimodal, bimodal, multimodal, uniform).
- center
- a measure that describes where the middle of the distribution is. The center is a number that describes a typical value. For example, one way to think about center is that it could be the point in the distribution where about half of the observations are below it and half are above it.
- spread
- a measure of how far apart the data are. In this lesson, the range is used to measure spread. The range is the difference between the maximum value and minimum value.
- outlier
- unusual observations that are outside the general pattern of the distribution.
- skew/skewness
- a visual difference from symmetry in a dataset.
- modality
- the number of peaks in the description of the shape in a dataset.
- unimodal
- one prominent peak in the distribution.
- bimodal
- two prominent peaks in the distribution.
- multimodal
- three or more prominent peaks in the distribution.
- uniform
- no prominent peaks in the distribution.
- range
- the difference between the minimum and maximum values in the dataset.
- symmetric
- the left and right sides of the distribution (closely) mirror each other. If you drew a vertical line down the center of the distribution and folded the distribution in half, the left and right sides would closely match one another.
- left-skewed
- the visual distribution where the left side has a longer tail.
- right-skewed
- the visual distribution where the right side has a longer tail.
Put formal DCMP I Can statements to prepare for the self-check.
These I Can Statements are new (the first three are the “you will understand” rephrased as an I Can):
- I can use common statistical language to describe a distribution based on what is observed from a graphical display.
- I can identify the description of a distribution of a quantitative variable including the shape, center, spread, and presence of outliers.
- I can identify a range as a misleading representation of spread for distributions that are skewed and/or contain outliers.
- I can describe the distribution of a quantitative variable using the shape, center, spread, and presence of outliers.
- I can identify an appropriate representation of the spread based on the shape of the distribution and presence of outliers.
