6.SP.A.2 6th Grade Statistics & Probability

Understanding Distributions

Understand that a set of data collected to answer a statistical question has a distribution described by its center, spread, and overall shape.

How to explain it

At this standard, students understand that data collected to answer a statistical question form a distribution, and will describe that distribution three ways: its center (where values cluster), its spread (from lowest to highest), and its overall shape (symmetric, skewed, uniform, with peaks, gaps, or outliers).

The anchor students hold onto: Describe any distribution three ways: CENTER (where values cluster), SPREAD (lowest to highest), and SHAPE (symmetric, skewed, peaks, gaps, outliers).

Describing a distribution by center, spread, and shape sets up choosing and computing measures of center and variability (6.SP.A.3).

Worked examples

Example 1 Center

Dot plot peaks at 2. Center?

Step 1Where data clusters = center

Step 2Tallest stack of dots is at 2

Step 3Most students own about 2 pets

Step 4Center is 2 — typical value

AnswerCenter is 2 — the typical value

Example 2 Spread

Ages dot plot: 9 to 14. Spread?

Step 1Spread = lowest to highest

Step 2Lowest age is 9, highest is 14

Step 3Values reach from 9 to 14

Step 4Spread: 9 to 14 (range of 5)

AnswerSpread: 9 to 14 (range of 5)

Common mistakes

What students write A dot plot with a long tail on the right side is called skewed left

The fix Skew is named for the TAIL direction — tail pointing right = skewed right.

What students write A data set has no spread if the center is a single number

The fix Center and spread are different features — spread is the range from lowest to highest, regardless of what the center is.

Teacher tip

Head off the two predictable errors before they happen. First: Skew is named for the TAIL direction — tail pointing right = skewed right. Second: Center and spread are different features — spread is the range from lowest to highest, regardless of what the center is.