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Week 10 Β· Models and Simulations

Wednesday

Count Lab: Roll the line
// Can a simple model predict what will happen next?
⏱ about 20 min

Wednesday: Count Lab: Roll the Line

Count Lab day. Comet clears the big workbench and sets the die in the middle.

"Thirty-six rolls," she says. "Let's see if the first rule matches Wren's log."

Wren lays his log beside the die: 18 arrivals in 6 hours. "What do you notice about the rule's guess?"

Comet counts on her fingers. "It expects 12. That is 6 short."

"Only if the rolls agree with the math," Wren says. "Let's roll and find out."

Nova hovers above the bench and projects a tally grid with six rows. "Would you like a hint?" she asks. "Write your prediction before the first roll. Then the dice cannot change your mind."

Comet hands you the die. "Data analyst, you roll first."

Your mission

You will run the first rule for all 36 slots, then compare your total with the prediction and with Wren's log.

Simulations are most useful when real experiments are hard to run. The thing may be too big, too small, too fast or too slow.

Random numbers can stand in for the variety in the real world. Your die stands in for the way people arrive at different times.

  • One die. No die? Number six paper slips from 1 to 6 and put them in a cup.
  • A pencil and a sheet of paper
  • A ruler and graph paper (or lined paper) for the graph
PREDICT BEFORE YOU ROLL
  • Read the question.
  • Tap your answer.
About how many arrivals does the first rule expect in 36 slots?
How many arrivals does Wren's log show?
How many more arrivals did the log show than the first rule expects?
  1. On paper, write Hour 1 to Hour 6 down the left side.
  2. For Hour 1, roll the die six times, once for each 10-minute slot.
  3. Each time you roll a 1 or a 2, make one tally mark next to that hour.
  4. A 3, 4, 5 or 6 means nobody arrived in that slot. Make no mark.
  5. If you use paper slips, put each slip back in the cup and shake it before the next draw.
  6. Repeat for Hours 2 to 6, so you roll 36 times in all.
  7. Count the tally marks for each hour, then add the six hour totals.
  8. Write your total next to the prediction (12) and Wren's log (18).
HourWren's log (made-up data from the Commons Count story)First rule expects aboutYour tally
Hour 122(your count)
Hour 232(your count)
Hour 332(your count)
Hour 442(your count)
Hour 532(your count)
Hour 632(your count)
Total1812(your total)
After you rollTrue or false?
Wren's log is higher than the first rule's prediction in five of the six hours.?
Two people running the same rule can get different totals.?
One run of 36 rolls proves the rule is right or wrong for good.?
The die stands in for the real-world variety in when people arrive.?
WHY THIS EXERCISEReading a simulation's results with care is as important as running it.
On graph paper, draw a bar graph of your six hour totals beside Wren's log. Start the y-axis at 0 and add a title.

Great lab work, data analyst. Tomorrow you will turn the gap you found into a hypothesis and fix the rule.

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