7.SP.3: Compare the Overlap of Two Distributions
Also written as 7.SP.B.3 and CCSS.MATH.CONTENT.7.SP.B.3 · Cluster: Draw informal comparative inferences about two populations.
The Official Wording
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
Common Core State Standards, Grade 7, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 7.SP.3 Means in Plain English
Seventh graders compare two dot plots by measuring the gap between their centers in units of spread. A glider averaging 69 ft and a dart averaging 60 ft, each with a mean absolute deviation of 3 ft, sit 9 ÷ 3 = 3 MADs apart, so the plots barely overlap.
A gap of 3 MADs is a visible difference; a gap of half a MAD would be mostly overlap. 7.SP.4 makes these comparisons from random samples, and high school compares center and spread using standard deviation (HSS-ID.2).
7.SP.3 I Can Statements
- I can find the mean and MAD of two data sets.
- I can express the gap between two means as a number of MADs.
- I can describe how much two dot plots overlap.
7.SP.3 Worked Example
Two paper airplane designs, ten flights each: the gap between their means is measured with the MAD as the ruler.
Two paper airplane designs were each flown 10 times. Distances in feet: Dart 54, 56, 57, 58, 60, 60, 62, 63, 64, 66. Glider 64, 65, 66, 66, 69, 69, 70, 72, 74, 75. How far apart are the two distributions?
- Find each center. Both designs have 10 flights.Dart mean = 600 ÷ 10 = 60 ft; glider mean = 690 ÷ 10 = 69 ft
- Find each spread with the mean absolute deviation: the average distance of a flight from its own mean.Dart MAD = 30 ÷ 10 = 3 ft; glider MAD = 30 ÷ 10 = 3 ft
- The spreads match, so 3 ft is a fair ruler for the gap between the centers.69 − 60 = 9 ft, and 9 ÷ 3 = 3 MADs
- Picture both dot plots on one number line. The only shared stretch is 64 to 66 ft.Overlap 64 to 66 ft: 2 dart flights, 4 glider flights
- Interpret: a gap of 3 MADs with a thin overlap is a real difference in how far the designs fly.The glider flies about 9 ft farther, 3 MADs
Check it: Deviations should balance around each mean. For the dart, 6 + 4 + 3 + 2 = 15 ft below 60 and 2 + 3 + 4 + 6 = 15 ft above, so 60 is right and the MAD is 30 ÷ 10 = 3.
Common Mistakes with 7.SP.3
Comparing centers without the spread
The means differ by 9 ft, so the glider is far better
Try this: Divide the gap by the MAD before judging: 9 ft is 3 MADs here, but only half a MAD if the MAD were 18 ft.
Using the range as the ruler
The dart’s range is 12 ft, so a 9 ft gap is under one range and means nothing
Try this: Measure spread with the MAD, which uses every flight; the range depends on just two flights, and one wild throw stretches it.
Expecting zero overlap from a real difference
One dart flight beat some glider flights, so the designs are the same
Try this: Look at where most of each plot sits; a few shared values are normal even when the centers are 3 MADs apart.
Where 7.SP.3 Fits
Practice 7.SP.3
Quick Check
- Two data sets have means of 40 and 46, and both MADs are 4. How many MADs apart are the centers?
- Team A’s mean height is 150 cm and team B’s is 152 cm, each with a MAD of 8 cm. Would the dot plots overlap a lot or a little?
- Find the MAD of 10, 12, 14, 16, 18.