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Statistics 9-12 / Week 04 / Wednesday
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Week 04 · Scatter Plots and Lines of Fit

Wednesday

Data Lab: the stride timing
// Weeks of practice against laps run
⏱ about 20 min

Wednesday: Data Lab, the Stride Timing

"Lab day," Comet says, setting cones along the park loop at 5, 10, 15, 20, 25, 30 strides.

"Walk from the start to each cone," Wren says. "I time it. One pair of numbers per cone."

Comet walks to the first cone. "4 seconds," Wren calls. She walks to the second. "8."

Six cones, six times. Nova plots them as Wren reads. "30 strides, 22 seconds. Would you like a hint? Look at the shape."

"Almost a perfect line," Comet says. "Steady walking makes a steady slope. What do you notice, Wren?"

"The slope is about 0.7 seconds per stride," he says. "And the intercept is near zero, which makes sense."

"Zero strides, zero seconds," Comet says. "The intercept has a meaning here. It did not on the practice chart."

What you need

  • A stopwatch or kitchen timer, a tape measure or six markers (cones, sticky notes or chalk marks).
  • Graph paper, a pencil and your Run Log.
  • A partner to hold the stopwatch, and a grown-up who knows where you are.
Safety first
Walk or jog on the park loop or a safe path with a grown-up aware. Never on a road.
Water is at hand. Stop and rest if you feel out of breath.
Cut any paper markers with scissors on paper. Nothing heavy is lifted alone.

Run the lab

  1. Mark six spots along a safe path at 5, 10, 15, 20, 25, 30 of your own strides from the start.
  2. Walk at a steady pace from the start to the first mark. Your partner times it in whole seconds.
  3. Return to the start and walk to the second mark. Time it. Repeat for every mark.
  4. Write the six pairs (strides, seconds) in a table in your Run Log.
  5. Plot the six dots on graph paper, strides across and seconds up. Say direction, form, strength, strays.
  6. Lay a pencil through the dots by eye. Then use a calculator to find the least-squares slope and intercept.

The crew's lab table

Here are the crew's own six timings from Nova's Run Log. Yours will differ, and that is the point.

ConeStridesSeconds
154
2108
31511
42015
52519
63022
The crew's stride timing: six dots and a least-squares line of slope about 0.73 seconds per stride.

The crew's line is seconds = 0.73 × strides + 0.47. The slope says each stride takes about 0.7 seconds.

The intercept 0.47 is close to zero. At zero strides, no time has passed, so a small intercept makes sense.

READ THE LAB LINE
  • Read the question.
  • Tap your answer.
A scatter plot, Strides and seconds, strides across and seconds up, with 6 points and a fitted line of slope about 0.73.The crew's points are (5, 4), (10, 8), (15, 11), (20, 15), (25, 19), (30, 22). What is the slope of the least-squares line? (Round to 2 places.)
The least-squares line has slope 0.7. What does the slope mean here?
The crew's line is seconds = 0.73 × strides + 0.47. What does it predict for 40 strides? (Round to 1 place.)
Cone 3 was 15 strides in 11 seconds. What is its residual from the crew's line? (Round to 1 place.)
In the crew's lab, how many seconds did the walk to the 20-stride cone take? Type the number.
WHY THIS EXERCISEEach timing is one dot. The line is built from all six together.
StatementTrue or false?
Steady walking gives a scatter plot with a nearly straight line.?
In the stride timing, the intercept should be far from zero.?
22 - 4 = 18?
Your lab line should match the crew's exactly.?
WHY THIS EXERCISESeeing a line come out of your own stopwatch makes slope and intercept real.
Draw your six dots on axes labeled strides and seconds. Draw your by-eye line and mark its intercept.

Good lab work. Tomorrow you see why squares are the right gaps to add, and a residual plot judges the fit.

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