Grade 9 › G9U08 Statistics: Spread

Grade 9 › G9U08 Statistics: Spread › L3
GRADE 9 · ALBERTAOUTCOME AB-G9-9ST1

L3 · Box plots: building and reading

Learning goal

“I can build a box plot from a data set - box from Q1 to Q3, line at the median, whiskers to the most extreme non-outlier values, outliers as separate points - and I can read a box plot's five landmarks and say what each part represents.”

Box plot — a graph of the five-number summary on a number line: a box from Q1 to Q3 with a line at the median, and whiskers reaching out toward the extremes.
Whisker — the line segment from the edge of the box to the smallest (or largest) value that is NOT an outlier.
Outlier point — a value beyond the outlier limits, plotted as a separate dot; the whisker does not reach it.
Worked example

Ages of 12 volunteers: 15, 22, 19, 24, 21, 18, 26, 23, 20, 17, 25, 30. Step 1: Summarize first - a box plot is only ever the five numbers, drawn. Ordered: 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30. Median = (21 + 22) / 2 = 21.5. Lower half 15, 17, 18, 19, 20, 21 -> Q1 = (18 + 19) / 2 = 18.5. Upper half 22, 23, 24, 25, 26, 30 -> Q3 = (24 + 25) / 2 = 24.5. Step 2: Check for outliers before drawing whiskers: IQR = 6; limits are 18.5 - 9 = 9.5 and 24.5 + 9 = 33.5. No value is outside, so the whiskers will reach the true minimum and maximum. Step 3: Draw the axis from 14 to 31. Draw the box from 18.5 to 24.5. Draw a line inside the box at the median, 21.5. Step 4: Draw the left whisker from 18.5 down to 15, and the right whisker from 24.5 up to 30. No separate points. Describe the finished plot in words: "Axis 14-31; box from 18.5 to 24.5 with a line at 21.5; whiskers ending at 15 and 30; no outlier points." Say it plainly: build the summary, test for outliers, THEN draw - the outlier test decides where the whiskers stop.

Check yourself — explain it

Why must the outlier test come before the whiskers are drawn?

Paired problem — example still visible

Build the box plot for 8, 11, 13, 16, 18, 20, 22, 25 (already ordered) and describe it in words. -> Median = (16 + 18) / 2 = 17. Q1 = (11 + 13) / 2 = 12. Q3 = (20 + 22) / 2 = 21. IQR = 9; limits -1.5 and 34.5, so no outliers. Description: box from 12 to 21 with a line at 17; whiskers ending at 8 and 25; no outlier points.

Faded completion — last step is yours

"Data: 30, 34, 38, 42, 46, 50 (ordered). Summary: min 30, Q1 34, median 40, Q3 46, max 50; IQR = 12, limits 16 and 64 - no outliers. The box is drawn from ___ to ___, the line inside is at ___, and the whiskers end at ___ and ___." -> box 34 to 46; line at 40; whiskers end at 30 and 50

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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