Displaying and comparing data
Center and spread are two different questions. A statistical question expects variation in the answers (“how many hours do sixth graders sleep?”), unlike “how old am I?”. Students compute mean, median, and mode for center, and range, interquartile range (IQR = Q₃ − Q₁), and mean absolute deviation for spread. They build dot plots, histograms, and box plots from the five-number summary, and describe shape, skew, and outliers. The mean follows every point; the median does not — so when one value is far from the rest, the median is usually the better typical value, and students should be able to say why.
Specification · for a parent or teacher
- data-distributions-6
- Advanced Math 6 · Unit 13
- High School Math 1
- Applied
- 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
- 5 items
Students can
statistical vs non-statistical questions; mean, median, mode; range, IQR, MAD; dot plot, stem-and-leaf, histogram, box plot (five-number summary); describe skew and outliers.
Ready when
given a list, they produce a box plot and say whether the mean or the median is the better typical value, and why.
Formulas
Subtract, do not add.
Watch for
mean always “better”; IQR as ; histogram bars with gaps for continuous data.