Statistical thinking: Descriptive statistics
Descriptions
Students “describe and summarize numerical data sets,” including those presented in charts or graphs, “identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected" (“Grade 6,” CCSS, 40).
Common pitfalls
Students analyze descriptive statistics for common pitfalls.
- Confusing the measurement under consideration.
- Mistaking a precise number for an accurate number.
- Using a misleading time frame.
- Mistaking a descriptive statistic for a stereotype, particularly with reference to differences among sensitive groups.
Absolute and relative numbers
Student differentiate between absolute numbers and relative numbers, and evaluate them within their context.
- Absolute figures have intrinsic meaning, but they only make sense within a sense of scale (is 30 big or small?).
- Relative figures have meaning only in the context of the absolute number or in relation to other relative figures. How big is the “fastest growing” sector or segment of the population? A percentage change relative to a very low starting point can look very large. And a small percentage of a large number can be very large in absolute terms.
Index
Students recognize the value and limitations of an index.
- An index collapses complex information into one number, such as the Dow Jones Industrial Average, a Gini coefficient (often used to describe income inequality), or a passer rating in fantasy football.
- An index number is often imperfect and oversimplified; it depends upon the precise formula for creating it: what information is included, and how each piece of information is weighed.
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