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Assess Visual Overlap of Data Distributions

Students informally assess the degree of visual overlap between two data distributions displayed as dot plots or box plots. They express differences in terms of variability—for example, noting that two populations have similar centers but one has much greater spread.

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Assess Visual Overlap of Data Distributions

Grade 7 · Statistics and Probability · question 1 of 3

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20 rungs. A star at the top.

Bus ridersCar riders4567891011121314151617181920minutes to school

A class compared minutes to school for two groups in these dot plots. Which group has the greater median, if either?

Read both plots and compare.

How it is taught

0:00 of 4:07

A distribution shows how data values spread out.

MAD measures typical distance from the center.

Two sets can have the same spread.

Grade 7Grade 84567891011121314151617181920push-ups

Read it: Comparing two data sets

Class A's quiz scores have a mean of 8 and Class B's a mean of 10, each with a MAD of 2. The means are 10 − 8 = 2 apart, and 2 ÷ 2 = 1 MAD.

  1. Read where each plot starts and ends, and where its center sits.
  2. Compare them: which center is higher, and how much of the scale both plots cover.
  3. For the gap, divide the distance between the means by the MAD: that many MADs apart.

A gap of 2 means more when the dots are packed close than when they spread wide.

The MAD measures the spread, so a gap counted in MADs compares the centers fairly.

Means less than 1 MAD apart overlap a lot; sets that share no value do not overlap at all.

MADs apart = the gap between the means ÷ the MAD.

Giving the gap itself, 2, as the number of MADs.

Divide the gap by the MAD: 2 ÷ 2 = 1 MAD apart.

Two classes' quiz scores have means of 14 and 22, and each has a MAD of 2. How many MADs apart are the means? — 4. The gap is 22 − 14 = 8, and 8 ÷ 2 = 4 MADs.

Class A vs Class B test scores

Two classes took the same math test. Let's see how their scores compare.

Here are Class A's six scores on a dot plot.

And here are Class B's six scores.

Class A's scores cluster right around eighty.

Class B's scores also center on eighty.

Both classes have about the same center — eighty points.

Class A's scores stay between seventy-five and eighty-five — a range of just ten points.

But Class B's scores stretch from sixty all the way to one hundred — a range of forty points!

Same center, very different spread. Class B has much greater variability.

Two classes, same testHow do their scores compare?Class A60100708090Class B60100708090Both centers ≈ 80Range = 10Range = 40TAKEAWAYSamecentervery different spread
Grade 7 · Same center, very different spread

When two distributions overlap, compare both their centers and their spreads.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Assess Visual Overlap of Data Distributions — Grade 7 Mathematics