Measures of Center and Spread
I can find and compare mean, median, range, IQR and standard deviation, and say which one fits the data.
The problem this sheet solves
Students meet average as a synonym for typical years before they meet a skewed data set, and the word is never corrected. One extreme value drags the mean and leaves the median where it was. The same confusion runs through spread: the range is a statement about two people, not about a group. The fastest demonstration in the lesson costs one sentence — change the outlier to a thousand times itself and ask what happens to each measure. The mean runs away; the median does not move, because there are still four values on each side. Standard deviation is COMPUTED here rather than gestured at, on a set built so every step lands whole, and the sheet is explicit that measures come in pairs: median with IQR, mean with standard deviation.
The key rule
One extreme value moves the mean a long way and does not move the median at all. Pair the median with the IQR, or the mean with the standard deviation.
Which one is anybody?
Watch out
The mistake: A student reports the average pay at this firm as 50 thousand.
The fix: Seven of the eight people earn less than 50. The mean is correct arithmetic and a false description. The median, 27.5, sits among the real numbers.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.