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
Part no.
data-distributions-6
Course
Advanced Math 6 · Unit 13
Also in
High School Math 1
Realm
Applied
Difficulty
3 of 4 Grade 6–7 core. Multi-step, first symbolic work.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

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

Mean
xˉ=xin\bar x = \frac{\sum x_i}{n}
Interquartile range
IQR=Q3Q1IQR = Q_3 - Q_1

Subtract, do not add.

Mean absolute deviation
MAD=xixˉnMAD = \frac{\sum \lvert x_i - \bar x \rvert}{n}

Watch for

mean always “better”; IQR as Q3+Q1Q_3+Q_1; histogram bars with gaps for continuous data.

Before · requires

After · used by

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data-distributions-6

Items: data-distributions-6-01 · data-distributions-6-02 · data-distributions-6-03 · data-distributions-6-04 · data-distributions-6-05