6.SP.B.5 6th Grade Statistics & Probability

Numerical Data Summaries

Summarize numerical data sets in relation to their context, reporting the number of observations and describing center and variability.

How to explain it

Students summarize a numerical data set in context: they report the number of observations, describe the attribute measured and its units, and compute a measure of center (mean or median) together with a measure of variability — the interquartile range or the mean absolute deviation. Students relate the choice of center and spread to the shape of the distribution, using the median and IQR for skewed data and the mean and MAD for symmetric data.

The anchor students hold onto: Pair a center with a spread: median with IQR (Q3 − Q1), or mean with MAD (the average absolute distance from the mean).

Computing the IQR and MAD completes the 6th-grade statistics strand and prepares students to compare two populations using these summaries in 7th grade (7.SP.B.3, 7.SP.B.4).

Worked examples

Example 1 IQR

Q1 = 20, Q3 = 40. Find IQR.

Step 1IQR = Q3 − Q1

Step 2= 40 − 20

Step 3= 20

AnswerIQR = 20

Example 2 MAD & Choose

Symmetric data: 3, 5, 7, 9.

Step 1Mean = 24 ÷ 4 = 6

Step 2Distances: 3, 1, 1, 3 → sum 8

Step 3MAD = 8 ÷ 4 = 2

Step 4Symmetric → mean & MAD

AnswerMAD = 2; use mean & MAD

Common mistakes

What students write Computing the IQR as max minus min (the range) instead of Q3 minus Q1.

The fix IQR = Q3 − Q1. It measures the spread of the middle half, not the full range.

What students write Always using mean and MAD even when data is skewed or has outliers.

The fix Outliers pull the mean. When data is skewed or has outliers, use median and IQR instead.

Teacher tip

Head off the two predictable errors before they happen. First: IQR = Q3 − Q1. It measures the spread of the middle half, not the full range. Second: Outliers pull the mean. When data is skewed or has outliers, use median and IQR instead.