Math 1 · Unit 12
Descriptive Statistics
Five lessons: pictures of data and their shapes, center (the mean and the median), spread (the IQR and the standard deviation), outliers and what they do, and comparing data sets. One quantity at a time, and the same three questions every time: what shape, where is the center, how spread out? The shape picks the statistics.
Pictures of Data and Their Shapes
One quantity at a time. The three pictures and what each is good for, the 5-number summary behind a box plot, and the shapes: symmetric, skewed right, skewed left, named by the tail. The songs data three ways, with a bin-width slider.
Start Unit 12, Lesson 1Center, the Mean and the Median
Where is the center? The mean is the balance point, add and divide; x-bar for a sample, mu for a population. The median is the middle value in order. Slide one class period out to 100 minutes and watch the mean move while the median stays: the median is resistant, so skewed data is described with the median.
Start Unit 12, Lesson 2Spread, the IQR and the Standard Deviation
How spread out is it? The IQR, the width of the box, resists extreme values. The standard deviation squares each distance from the mean, averages, and takes the square root, the same move as the distance formula. Worked once by hand on 2, 4, 6, 8, 10, then the tool. Sigma for everyone, s for a sample.
Start Unit 12, Lesson 3Outliers and What They Do
The rule: IQR times 1.5, subtracted from Q1 and added to Q3, gives the fences; anything past a fence is an outlier. Add a 74 inch player to the basketball team and watch the mean and standard deviation move while the median and IQR stay put. Outliers pull the mean; the median resists.
Start Unit 12, Lesson 4Comparing Data Sets
Put it all together. Same scale, shape first, the statistics that fit the shape, then sentences in context. Two classes with the same mean turn out different: one scored higher by the median, the other was far more consistent by the IQR. Then recommend a fertilizer from three.
Start Unit 12, Lesson 5Printables for Unit 12
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.