Statistics: center and spread

Practice 5 items →

Center and spread, now with standard deviation. Students compute the five-number summary, mean, and s or σ by hand for a short list, apply the 1.5 × IQR outlier fence, and predict how shifting or scaling the data changes each statistic.

Specification · for a parent or teacher

Part no.: descriptive-stats-spread
Course: High School Math 1 · Unit 17
Realm: Applied
Difficulty: 4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
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

compute the five-number summary, $\bar x$ , and $s$ or $\sigma$ by hand for a short list; apply the $1.5\times IQR$ fence; predict how a shift or scale changes each statistic.

Ready when

from a list they give five-number summary, $s$ or $\sigma$ as required, and name the outliers.

Formulas

Population SD

\sigma = \sqrt{\frac{\sum (x_i - \bar x)^2}{n}}

Outlier fence

[\,Q_1 - 1.5\,IQR,\ Q_3 + 1.5\,IQR\,]

Watch for

$\sigma$ computed without the square root; outlier rule as $IQR$ beyond the min/max.

Before · requires

Data handlingdata-handling-7 · Math 7
Real numbersreals-radicals-sci-notation · Math 7

After · used by

Data analysis: two variablesbivariate-regression · Math 1

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