6.SP.3: Measures of Center and Variation
Also written as 6.SP.A.3 and CCSS.MATH.CONTENT.6.SP.A.3 · Cluster: Develop understanding of statistical variability.
The Official Wording
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.
Common Core State Standards, Grade 6, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 6.SP.3 Means in Plain English
Sixth graders sort summary numbers into two kinds. A measure of center, like the mean, gives a typical value: 10, 11, 12, 13, 14 and 2, 7, 12, 17, 22 both average 12. A measure of variation, like the range, says how much values differ: 4 versus 20.
Knowing which job each number does keeps students from answering “how consistent?” with a mean. 6.SP.5 has them compute the median, mean, interquartile range and mean absolute deviation. In 7th grade they compare two groups by how far apart the centers are in units of the spread (7.SP.3).
6.SP.3 I Can Statements
- I can use one number, like the mean, to stand for a data set.
- I can use one number, like the range, to say how much values vary.
- I can tell a measure of center from a measure of variation.
6.SP.3 Worked Example
Two players with identical averages and nothing else in common, told apart by a second kind of number.
Two players scored these points in five games. Ana: 10, 11, 12, 13, 14. Ben: 2, 7, 12, 17, 22. Who scores more on a typical night, and who is more consistent?
- A measure of center stands in for all five games with one number. Find each player’s mean.Ana: 60 ÷ 5 = 12. Ben: 60 ÷ 5 = 12.
- Same mean, and the median is 12 for both, so a center alone cannot tell them apart. Look at how far each game sits from the mean.Ana: 2, 1, 0, 1, 2 away. Ben: 10, 5, 0, 5, 10 away.
- A measure of variation sums up those distances with one number. The mean absolute deviation is their average.Ana MAD = 6 ÷ 5 = 1.2. Ben MAD = 30 ÷ 5 = 6.
- Now two numbers tell the whole story: same typical score, very different consistency.Center 12 and 12; variation 1.2 and 6.
Check it: The range agrees: Ana’s scores span 14 − 10 = 4 points, Ben’s span 22 − 2 = 20. Any measure of variation should rank Ben as more spread out.
Common Mistakes with 6.SP.3
Treating the mean as the whole story
“Both players average 12, so they are the same.”
Try this: Put both sets on one number line and ask which player you would bet on to score at least 10; the spread decides it.
Calling the range a center
“Ben’s center is 20 because 22 − 2 = 20.”
Try this: Sort the measures into two boxes on the board, center and variation, and state what each one answers: where, or how far apart.
Averaging signed deviations
Ben: −10 − 5 + 0 + 5 + 10 = 0, so MAD = 0
Try this: Measure distance, not direction: write each deviation as a positive number of points away from the mean, then average those.
Where 6.SP.3 Fits
Practice 6.SP.3
Quick Check
- Find the mean of 14, 9, 11, 16, 10.
- Which is a measure of variation: a median of 6 or a range of 6?
- Set A: 20, 20, 20, 20. Set B: 10, 15, 25, 30. Compare their means and their spreads.