Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A data set can contain dozens of values, and sometimes we need to sum them up quickly. A measure of center does that with a single number that represents a typical value: the mean (the fair-share average) or the median (the middle value when the data are in order). A measure of variation also uses a single number, but it tells you something different: how much the values differ from one another. The range, the interquartile range and the mean absolute deviation are all measures of variation.
Sixth graders need to recognize the job each kind of measure does. Two basketball teams can both average 60 points per game, yet one scores between 58 and 62 every night while the other swings from 40 to 80. The centers match; the variation does not. Knowing the center without the variation, or the reverse, gives an incomplete picture. This standard is about recognizing that difference; computing the interquartile range and the mean absolute deviation is developed further in 6.SP.B.5.
The median is the middle of the ordered list. Taking the middle of an unordered list gives a random value.
The mean of 2, 3 and 6 is 11/3, about 3.67, which is not in the list. A center summarizes values; it need not be one of them.
A range of 20 does not mean values are around 20. It means the highest and lowest are 20 apart.
Team A scored 58, 60, 61, 59, 62 points. Team B scored 40, 80, 55, 65, 60. Find the mean and range for each team and compare.
Answer: Both teams have a mean of 60, but Team A's range is 4 and Team B's range is 40, so Team B varies much more.
Let students build both measures with cubes: leveling towers to equal heights shows the mean, and lining towers up in order shows the median. Comparing data sets with matched centers but different spreads makes the need for variation obvious.
Assessments ask students to identify which measure is a center or a variation, compute simple means, medians and ranges, and interpret them in context.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 7
Total = 35, and 35 ÷ 5 = 7.
Answer: 11
Order: 4, 7, 9, 13, 15, 21. The two middle values are 9 and 13, so the median is (9 + 13) ÷ 2 = 11.
Answer: B) Interquartile range
The interquartile range describes how spread out the middle half of the data is. The other three describe center.
Answer: 22
Range = 40 - 18 = 22.
Answer: D) A measure of variation such as the range or IQR
Equal centers can hide very different spreads. A measure of variation shows how consistent each class was.
A full lesson with slides, activities and an exit ticket on measures of center and variation, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.SP.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn measures of center and variation into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A measure of center gives a typical value for the data. A measure of variation tells how spread out the values are. Both are single numbers, but they answer different questions.
Center: mean and median. Variation: range, interquartile range and mean absolute deviation.