6.SP.2: Center, Spread and Shape of a Distribution
Also written as 6.SP.A.2 and CCSS.MATH.CONTENT.6.SP.A.2 · Cluster: Develop understanding of statistical variability.
The Official Wording
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Common Core State Standards, Grade 6, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 6.SP.2 Means in Plain English
Sixth graders describe a whole data set, not one value. Eleven homework times from 15 to 90 minutes go on a number line as dots, and students describe the picture: center (median 30), spread (most values 15 to 45) and shape (one cluster plus a far-out 90).
The three words become the vocabulary of the strand. 6.SP.3 pins center and spread to single numbers, 6.SP.4 draws the shape as dot plots, histograms and box plots, and 6.SP.5 writes the full summary. In 7th grade students compare two distributions this way (7.SP.3).
6.SP.2 I Can Statements
- I can find the center of a data set with the median.
- I can describe how spread out a data set is.
- I can describe the shape: clusters, peaks, gaps and far-out values.
6.SP.2 Worked Example
Eleven homework times on a number line, described three ways, with one stubborn 90 showing what an outlier does to spread.
Eleven students reported last night’s homework time in minutes: 15, 20, 25, 30, 30, 30, 35, 35, 40, 45, 90. Describe the distribution.
- Put the data in order and plot it on a number line, one dot per student. The picture is the distribution.15, 20, 25, 30, 30, 30, 35, 35, 40, 45, 90
- Center: the median is the middle value. Eleven values, so the 6th one.Median = 30 minutes
- Spread: how far the values run. The range is largest minus smallest, but notice how different it is with and without the 90.Range = 90 − 15 = 75; without the 90 it is 45 − 15 = 30
- Shape: look at where the dots pile up and where they thin out.Cluster from 15 to 45, peak at 30, gap from 45 to 90, one value far to the right
- Say it in context, in a sentence a parent would understand.A typical student spent about 30 minutes; most spent 15 to 45, and one spent 90.
Check it: Cover the 90 with a thumb and look again: the median of the remaining 10 values is still 30, so the center held steady while the spread changed a lot. That is what one far-out value does.
Common Mistakes with 6.SP.2
Describing a distribution with one number
“The data is 30.”
Try this: Ask three questions every time: where is the middle, how far do the values stretch, and what does the pile of dots look like?
Reading the middle of the axis as the center
The line runs 0 to 100, so the center is 50
Try this: Count dots, not inches: the median splits the students into two halves, and it lands at 30, not at the midpoint of the axis.
Mixing up shape with spread
“The shape is 75.”
Try this: Give shape words to use: one cluster or two, symmetric or leaning one way, gaps, and a value far from the rest.
Where 6.SP.2 Fits
Practice 6.SP.2
Quick Check
- Find the median of 8, 3, 12, 5, 9, 7, 3.
- Two classes took a 10-point quiz. Class A: 7, 7, 8, 8, 8, 9. Class B: 4, 6, 8, 8, 10, 10. Which class has the greater spread?
- Shoe sizes in a class: 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 11. Describe the shape in one sentence.