Measures of Center and Spread
I can find the mean, median, IQR and standard deviation, and say which pair describes the data.
What students learn
Students learn to find the mean, the median, the IQR and the standard deviation, see how one value far from the rest moves the mean but not the median, and pair each center with its spread.
See inside
The key rule
The mean adds every value, so one value far from the rest pulls it toward that value. The median depends only on the middle of the ordered list.
SD = √(mean of the squared deviations)
Pair the median with the IQR, and the mean with the SD. With no far values and a balanced shape, the mean and SD usually fit best.
Watch out
Eight salaries, in thousands of dollars: 22, 24, 25, 27, 28, 30, 33, 211. A student calls the mean, 50, the typical salary.
The mistake: typical salary: the mean, 50Seven of the eight earn less than 50.
The fix: typical salary: the median, 27.5211 pulls the mean; the median sits among the salaries.
The mistakes it targets
- Calls the mean typical when one value is far from the rest
- Takes the median of an unsorted list
- Gives the range as the IQR
- Stops before taking the square root for the standard deviation
- Pairs the median with the range instead of the IQR
- Averages the deviations without squaring them
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, six common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.