Summarize numerical data sets in relation to their context, such as by:
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A complete data summary tells a reader four things, and this standard lists them. How many observations there are. What was measured, how it was measured and in what units. Numerical measures of center (median or mean) and of variability (interquartile range or mean absolute deviation), plus any overall pattern and any striking departures from it. And finally, why those particular measures were chosen given the shape of the data and the situation.
The last point separates a mechanical answer from a thoughtful one. When data are roughly symmetric with no outliers, the mean and mean absolute deviation (MAD) describe them well. When data are skewed or contain an outlier, such as one very high house price in a neighborhood, the median and interquartile range (IQR) are more representative, because they are not pulled by extreme values. Sixth graders compute the MAD by finding how far each value is from the mean and averaging those distances, and the IQR by subtracting the lower quartile from the upper quartile. The context always matters: a summary should talk about minutes, points or dollars, not just numbers.
One very large value pulls the mean upward. For incomes or house prices with an outlier, the median better reflects a typical value.
Differences from the mean always add up to zero, so students must use distances (absolute values) before averaging.
A summary that says 'mean 12, MAD 2' does not say 12 of what. Units and context are part of the standard.
Five students recorded minutes spent on homework: 20, 30, 25, 35, 40. Find the mean and the mean absolute deviation, and summarize.
Answer: For 5 students, a typical homework time was 30 minutes, and times varied from the mean by 6 minutes on average.
Give students a writing frame with the four parts (count, attribute and units, measures and pattern, justification) and have them summarize real class data. Comparing summaries of a symmetric set and a skewed set shows why the choice of measure matters.
Assessments may ask for a single measure, or for a short written summary that names the measures and explains the choice. MAD and IQR calculations with small data sets are common.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 8
Lower half 2, 4, 5, 7 has median 4.5. Upper half 9, 11, 14, 16 has median 12.5. IQR = 12.5 - 4.5 = 8.
Answer: 2.4
The mean is 10. Distances from 10: 4, 2, 0, 2, 4. Their mean is 12 ÷ 5 = 2.4.
Answer: C) Median and IQR
The mansion is an outlier that would pull the mean and MAD. The median and IQR are resistant to outliers.
Answer: 24
Each student gives one observation, so there are 24 observations.
Answer: A) Signed differences from the mean always add up to zero
Values above and below the mean cancel out exactly, so averaging signed differences always gives 0.
A full lesson with slides, activities and an exit ticket on summarizing data sets in context, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.SP.B.5 with an answer key, ready in about a minute.
Make a worksheet →Turn summarizing data sets in context into a quiz students answer online that marks itself, with a class summary for you.
Build a test →The number of observations, what was measured and its units, measures of center and variability with any pattern or outliers, and a reason for the measures chosen.
When the data are skewed or include outliers. The median and IQR are not pulled by extreme values.