Grade 6 Math · Topic 72
When you summarize a data distribution, you describe its center, spread, and shape, plus any outliers. The right measures depend on the shape.
Lesson alignment: 6.SP.A.2 · 6.SP.B.5.d · Take your time. You can return to this lesson whenever you need it.
Explore visually
Compare the same data in a dot plot and a box plot, then summarize its center and spread.
Think first: How might the dot plot and box plot show the same center and spread?
Swipe horizontally to see the full diagram.
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Grade 6 core skill · 6.SP.B.5.d
Describe the shape and context before choosing summary measures. The mean and mean absolute deviation use every value and work well when a distribution is fairly balanced. The median and interquartile range are more resistant to an extreme value and often describe a skewed distribution better.
Most students report 40–90 minutes, but one response is 500 minutes. That extreme value pulls the mean upward. The median better represents a typical student, and the range or interquartile range can describe spread.
Ask: Is the distribution balanced, skewed, or affected by an outlier?
There is not one best measure for every data set. Explain how the distribution's shape and the question's context support your choice.
The mean and mean absolute deviation use all values and describe a balanced distribution well.
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 1
Start by writing the calculation clearly: 100 is an outlier (way above the rest). The mean is dragged up by it; the median is unaffected. Use the median.
Answer: Median
Worked example 2
Skewed right (a few large values stretch the tail toward larger numbers).
Answer: Skewed right
Work these on paper first. Open “Check” when you are ready to compare your answer.
Symmetric
Right-skewed
Left-skewed
40
2
Mean
Median
IQR
Salaries (in thousands): 30, 32, 35, 36, 38, 200. Should you report the mean or the median? Why?
Answer: Median.
Start by writing the calculation clearly: 200 is an outlier; it pulls the mean much higher than what most people earn. The median better represents a typical value.
A dot plot of test scores piles up on the right with a long tail toward low scores. Describe the shape.
Answer: Skewed left.
Tail extends to the left (low values), so the distribution is left-skewed.
Fresh questions · saved on this device
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
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