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Data and Society 9-12 / Week 09 / Mission Quest
6/6
Week 09 · Finding the Middle and the Pattern

Mission Quest

Mission Quest: Roll for the Middle
// Typical values, extreme values and what a pattern can prove
⏱ about 20 min

Mission Quest: Roll for the Middle

The crew meets at the Commons game shelf on Saturday morning.

Comet rattles a die in her hand. "If we roll this fifteen times, what is the typical roll?"

Wren writes three words on a card: mean, median, mode. "What do you notice? We can find all three."

"Do you think they will match?" he asks.

Nova hovers over the table. "Would you like a hint?" she asks. "Write every roll before you start adding. A list is easier to sort than a memory."

Comet grins and rolls. "Three! Write it down!"

  1. The mean is the sum of the values divided by how many there are.
  2. The median has half the data below it and half above it. Sort first.
  3. The mode is the value that appears most often. There can be more than one.
  4. Extreme values pull the mean toward the long tail, so all three values can be useful.
  5. A correlation does not prove a cause. Combine sources before you conclude.
  6. The same median algorithm works in many fields.
◇ ROLL FOR THE MIDDLE
You need paper, a pencil and one die.
No die? Number six paper slips from 1 to 6 and put them in a cup.
With a slip cup, draw one slip, write its number, and put it back before the next draw.
Take turns with a family member. Roll or draw 15 times in all.
Write each result in a row as you go.
Sort the 15 results from smallest to largest.
Add them up and divide by 15 to find the mean. It is fine to round to one decimal place.
Find the 8th value in your sorted list. That is the median.
Find the value that appears most often. That is the mode, and there may be more than one.
First, practice on the crew's 15 rolls in the table after this box. Then do your own.
Crew practice rolls (made-up)Results
Rolls in order3, 2, 6, 1, 2, 4, 3, 5, 2, 1, 6, 3, 2, 4, 1
Sorted1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6
For a grown-up
This week your student learned the mean, median and mode, and that a pattern does not prove a cause.
You only need one die, or six numbered paper slips in a cup.
Ask: which of your three values best describes a typical roll? Ask: did any value surprise you?
Everything in this course is done on paper. No app, website or account is needed.
QUEST CHECK (CREW PRACTICE ROLLS)
  • Read the question.
  • Tap your answer.
What is the sum of the crew's 15 rolls?
What is the mean of the crew's rolls?
What is the median of the crew's rolls?
What is the mode of the crew's rolls?

Amazing work this week, data analyst. Next week you will build a simple model and test whether it can predict.

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