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Statistics 9-12 / Week 02 / Wednesday
3/6
Week 02 · Outliers and the Normal Model

Wednesday

Data Lab: the shuttle walk with a stop
// One far lap, and a bell-shaped hill
⏱ about 20 min

Wednesday: Data Lab, the Shuttle Walk With a Stop

"Lab day," Comet says, placing two cones twenty steps apart on the grass by the bench.

"Shuttle walks," Wren says. "Cone to cone and back is one walk. Twelve of them, timed in whole seconds."

"And on one walk, stop for a sip of water at the far cone," Comet says. "On purpose. We want an outlier."

Comet walks, Wren clicks, Nova logs. "21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 26, 38 seconds. The water stop was the 38."

"Fences," Wren says, working fast. "Q1 22.5, Q3 25, IQR 2.5. Upper fence 28.75. The 38 is an outlier."

Nova shows both means. "With it, 24.7. Without it, 23.5. Would you like a hint? Check the median too."

"23.5 with, 23 without," Comet says. "It moved by half a second. Now you run yours."

What you need

  • A stopwatch or kitchen timer and two markers for cones (shoes or sticks work).
  • Graph paper, a pencil and your Run Log. A cup of water at the far marker.
  • A grown-up who knows where you are.
Safety first
Walk, do not run, on the park loop or a safe path at home. Never on a road or near traffic.
A grown-up knows where you are and water is at hand. Stop and rest if you feel tired or too warm.
Any cutting is scissors on paper or cardboard. Nothing heavy is lifted alone.

Run the lab

  1. Set two markers about twenty steps apart. One shuttle walk is out to the far marker and back.
  2. Time twelve shuttle walks in whole seconds. On one of them, pause at the far marker for a sip of water.
  3. Write the twelve times in order. Find Q1, Q3 and the IQR.
  4. Find both fences. Mark any value outside them as an outlier.
  5. Find the mean and median with every value, then again without the outlier. Record all four.
  6. Draw the dot plot and mark the fences with dashed lines.

The crew's lab table

The crew's twelve shuttle walks are made up for the Run Log. Yours will differ, and that is the point.

Walk123456789101112
Seconds212222232323242425252638
A dot plot of twelve shuttle walks from 21 to 38 seconds, with one far dot at 38.
MeasureWith the water stopWithout it
Mean24.723.5
Median23.523
Fences18.75 and 28.7517.5 and 29.5
READ THE LAB DATA
  • Read the question.
  • Tap your answer.
The shuttle walks have Q3 = 25 and IQR 2.5. What is the upper fence?
The shuttle walks are 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 26, 38. Which value is an outlier by the 1.5 × IQR rule?
The shuttle walks are 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 26, 38. Remove the outlier 38. What is the mean now? (Round to 1 place.)
The shuttle walks include the outlier 38. Which center and spread describe this set best?
The shuttle-walk lower fence is Q1 - 1.5 × IQR = 22.5 - 3.75. Type it.
WHY THIS EXERCISEBoth fences matter. A very fast walk could be an outlier on the low side.
A measure that barely moves when one value becomes extreme is called what? Type one word.
A value beyond a fence is called what? Type one word.
StatementTrue or false?
25 + 1.5 × 2.5 = 28.75?
The water stop should be reported as an outlier, not hidden in the mean.?
Removing an outlier always changes the median by a large amount.?
A normal model would fit the shuttle walks well, outlier included.?
WHY THIS EXERCISESeeing your own outlier move your own mean teaches more than any table.
Draw your dot plot of twelve shuttle walks with both fences as dashed lines and the outlier circled.

Good lab work. Tomorrow you prove why the median resists, and you learn when the normal model should not be used.

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