6.SP.A.3 6th Grade Statistics & Probability

Center vs Variability

Recognize that a measure of center summarizes a data set with a single number, while a measure of variation describes how the values vary.

How to explain it

At this standard, students find and compare two kinds of summary numbers: a measure of center (mean or median — the typical value) and a measure of variation (range — the spread). Students recognize that each is a single number summarizing the whole set and that center and variation answer different questions.

The anchor students hold onto: Find the CENTER with the mean or median (one typical number). Find the VARIATION with the range (one spread number).

Finding center and variation prepares students to compare data displays and to compute measures like the IQR and mean absolute deviation (6.SP.B.4 and 6.SP.B.5).

Worked examples

Example 1 Mean (center)

Mean of 4, 6, 8, 10, 12.

Step 1Add: 4+6+8+10+12 = 40

Step 2Count the values: 5

Step 3Divide: 40 ÷ 5 = 8

Step 4Mean = 8 (one typical number)

AnswerMean = 8

Example 2 Range (variation)

Range of 5, 8, 11, 14, 20.

Step 1Range = highest − lowest

Step 2Highest = 20, lowest = 5

Step 320 − 5 = 15

Step 4Range = 15 (one spread number)

AnswerRange = 15

Common mistakes

What students write A student claims two data sets with the same mean are identical because their centers match.

The fix Equal means do not guarantee equal spread — always check the range to assess variation.

What students write A student labels the range as a measure of center because it summarizes the data in one number.

The fix The range measures variation (spread), not center — it tells how spread out, not what is typical.

Teacher tip

Head off the two predictable errors before they happen. First: Equal means do not guarantee equal spread — always check the range to assess variation. Second: The range measures variation (spread), not center — it tells how spread out, not what is typical.