6.SP.5: Summarize a Data Set in Context
Also written as 6.SP.B.5 and CCSS.MATH.CONTENT.6.SP.B.5 · Cluster: Summarize and describe distributions.
The Official Wording
Summarize numerical data sets in relation to their context, such as by:
Common Core State Standards, Grade 6, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 6.SP.5 Means in Plain English
Sixth graders write the full report on a data set. For 11 bean plants, that means saying how many plants, what was measured and how, the median (15 cm) or mean (17 cm), the spread (IQR 7 cm), the pattern, and the 29 cm plant that stands out.
Part d is the judgment call: with one plant far above the rest, the median and IQR describe a typical plant better than the mean and MAD, which that plant drags upward. This caps the 6th-grade strand, and 7th grade reuses every piece to compare two populations (7.SP.4).
6.SP.5 I Can Statements
- I can report how many values there are and what was measured.
- I can find the median, mean, interquartile range and mean absolute deviation.
- I can choose the measures that fit the shape of the data.
6.SP.5 Worked Example
Eleven bean plants summarized the way the standard lists it, parts a to d, ending with a judgment about which measures to report.
A class measured 11 bean plants three weeks after planting, in centimeters from the soil to the tip of the tallest leaf: 12, 12, 13, 14, 14, 15, 18, 19, 20, 21, 29. Write a summary of the data.
- (a) Report how many observations there are. Count the values, not the students or the days.n = 11 plants
- (b) Say what was measured, how, and in what unit.Height in cm, soil to tip of the tallest leaf, with a ruler, on day 21
- (c) Give the center two ways. The median is the 6th of 11 ordered values; the mean is the total divided by 11.Median = 15 cm; mean = 187 ÷ 11 = 17 cm
- (c) Give the variability. The quartiles are the middles of the 5 values on each side; the mean absolute deviation averages each plant’s distance from 17.Q1 = 13, Q3 = 20, IQR = 7 cm; MAD = 44 ÷ 11 = 4 cm
- (c) Describe the pattern and anything that sticks out, in context.Two clumps, 12 to 15 and 18 to 21; one plant at 29 cm, the one on the windowsill
- (d) Choose the measures that fit the shape. One far-out value pulls the mean and the MAD up; the median and IQR ignore it.Report median 15 cm and IQR 7 cm as the typical plant and typical spread
Check it: Deviations from the mean must balance: below 17 they total 5 + 5 + 4 + 3 + 3 + 2 = 22, above 17 they total 1 + 2 + 3 + 4 + 12 = 22. The mean is right, and all 11 values are accounted for.
Common Mistakes with 6.SP.5
Numbers without units or context
“Median 15, mean 17, MAD 4.”
Try this: Require every number to carry its unit: “the median plant is 15 cm tall,” so the summary reads as a sentence about plants.
Always reaching for the mean
“The typical plant is 17 cm,” a height that lands in the gap between the two clumps
Try this: Look at the shape before choosing: a far-out value drags the mean toward it, so a skewed set is better described by the median.
Skipping the striking deviation
“Plants were 12 to 29 cm, median 15.”
Try this: Ask “what surprised you?” after the numbers; the summary should say that one plant was 8 cm taller than any other and guess why.
Where 6.SP.5 Fits
Practice 6.SP.5
Quick Check
- Find the mean and the mean absolute deviation of 4, 6, 8, 10, 12.
- Find the interquartile range of 3, 7, 8, 10, 12, 15, 20.
- House prices on a street, in thousands: 180, 190, 195, 200, 210, 950. Which center describes a typical house, and why?