6th grade shape of a distribution worksheets

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Shape of a distribution worksheets for 6th grade show dot plots and ask five yes-or-no questions about them. Do the counts mirror on both sides of the median? Is the mean above the median, with a longer right tail? Are at least three fourths of the values inside one 4-cm interval? Your child checks each claim against the dots and answers from the plot.

Free printable PDF worksheet, aligned to Common Core 6.SP.B.5.

Each print is a different sheet with its own answer key. You don't need to sign up.

The kind of problems you'll get

Use the dot plots to check symmetry, right skew, clusters, gaps, and outliers.

  1. Data: 2, 3, 4, 4, 5, 6.

    Answer: The data are symmetric around 4 and range from 2 to 6.

Most problems on this sheet sit beside a picture, model or diagram, so this is the worked example the sheet itself prints. The answer key on page two prints the answer under every problem.

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on each sheet

Every version prints on US Letter or A4, with its answer key after the problems.

This sheet is one of the versions on the 6th grade mean, median, mode & range page, with its own difficulty choices and its own answer key.

How to teach this

Have your child find the median dot first and put a finger on it. Most of the questions are checked from there. Symmetry means the dots on the left mirror the dots on the right, so count both sides. A longer right tail means the few far dots are on the high end, which drags the mean above the median. For a cluster question, the sheet gives the interval width, so count how many dots fall inside the best window and compare to the total. The trap is answering from the general look of the plot. A plot can look roughly balanced and still fail a strict mirror check by one dot. Have your child point to the dot that decides the answer. If they cannot point to it, count again.

Watch for: Kids call a plot symmetric because it has one hump in the middle. Symmetry is a mirror check: the count at each distance left of the center has to match the count at that distance on the right. Kids put the skew on the side with the tall stack. Skew is named for the tail, the thin stretch of far dots. A right skew has its tail on the right and its pile on the left.

Common questions about 6th grade shape of a distribution

What does my child actually write?
Yes or no, five times. Each question makes one exact claim about a dot plot: about symmetry, right skew, a cluster inside a stated interval, a gap, or an outlier. The Remember box on the sheet says to describe where data cluster and how widely they spread, and that a symmetric display balances around its center.
How is this different from the describing distributions sheet?
That sheet asks for a written summary with numbers: center, spread and shape in your child's own words. This one flips it. The claim is already written, and the job is to check it against the plot and say whether it holds. It is the faster sheet and a good one to do first.
Which standard is this?
6.SP.B.5, summarizing data sets in relation to their context, and specifically the part about describing the overall pattern and any striking departures from it. Five problems, one difficulty, new dot plots on every print.

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Aligned to Common Core 6.SP.B.5. Reviewed by the One more sheet team. Content version 241, updated September 2026.

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