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Statistics 9-12 / Week 02 / Track Day
6/6
Week 02 · Outliers and the Normal Model

Track Day

Track Day: find the outlier
// One far lap, and a bell-shaped hill
⏱ about 20 min

Track Day: Find the Outlier

Saturday at the park gate. Comet counts her steps from the gate cone to the fountain cone eleven times.

"19, 20, 20, 21, 21, 21, 22, 22, 23, 24, 32," Nova logs. "Would you like a hint? One of those is not like the others."

"I stumbled on the last one," Comet says. "32 steps. Fences first: Q1 20, Q3 23, IQR 3."

"Upper fence 27.5," Wren says. "So 32 is an outlier. Median 21, and the mean is 22.3."

"Without the stumble the mean is 21.3," Comet says. "The median is 21. Resistant, like we proved."

"Track Day," Wren says to a family at the gate. "Collect ten numbers at home, build the fences, find any outlier."

"What can we make?" Comet asks. "A poster sentence for your own data, with the outlier named."

  1. The 1.5 × IQR rule: fences at Q1 - 1.5 × IQR and Q3 + 1.5 × IQR. Values outside are outliers.
  2. Outliers pull the mean and standard deviation. The median and IQR resist, because the median looks at a position.
  3. The normal model: 68% within 1 standard deviation, 95% within 2, 99.7% within 3. z = (value - mean) ÷ standard deviation.
  4. Fit the bell only to symmetric, single-peaked data with no outlier. Every reading was the crew's own from Nova's log.
A dot plot of step counts from 19 to 32, bunched near 21 with one far dot at 32.
◇ YOUR TRACK DAY FENCES
Pick one number your family can collect at least ten times today, such as seconds to walk the hall.
Collect the values together and write them in order. Find Q1, Q3 and the IQR.
Find both fences. Circle any value outside them.
Find the mean and median with and without any outlier. Say which moved more and why.
Write one poster sentence for your data: the center, the spread and any outlier, in plain words.
For a grown-up
Any walking or stepping is indoors or on a safe path, never on a road. Water is at hand.
The numbers are the family's own readings, not facts about anyone else.
Cutting paper for number lines is scissors only. Nothing heavy is lifted alone.
TRACK DAY CHECK
  • Read the question.
  • Tap your answer.
Comet's step counts have Q3 = 23 and IQR 3. What is the upper fence?
Comet's step counts are 19, 20, 20, 21, 21, 21, 22, 22, 23, 24, 32. Which value is an outlier by the 1.5 × IQR rule?
Comet's step counts are 19, 20, 20, 21, 21, 21, 22, 22, 23, 24, 32. Remove the outlier 32. What is the mean now? (Round to 1 place.)
Comet's median step count with the stumble is 21. What is it without the stumble? Type the number.
WHY THIS EXERCISEShowing a family member that the median held still is the best proof of resistance.
Draw your family's dot plot with both fences as dashed lines and any outlier circled.

Track Day done. Next week: sign-up cards sorted by morning or evening and finished or stopped, in a two-way table.

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