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Lesson 10 of 11

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Eight questions, one for each idea. Read the table first if you want to.

Where a set of numbers balances, and what a line will not promise
IdeaHow it goes
Balance pointThe mean is the one point where readings balance.
The two sidesDistances above the mean total the same as below.
A moved readingThe mean moves by the move, shared among the readings.
A new readingAbove the mean it pulls up, below it pulls down.
Two groupsRebuild both totals, add them, then share by the total count.
Equal groupsTwo means average to the true mean when the counts match.
Joining dotsJoin dots when the bottom scale has a real order.
The side scaleWhere it starts changes how big a change looks.

The rule: Compare the new reading with the current mean. A reading above the mean raises the mean. A reading below the mean lowers it. A reading equal to the mean changes nothing.

Three library readings are 2, 4 and 9 books. Which point balances them?

  • 4, because one reading sits below it and one above
  • 5
  • 5.5, halfway between 2 and 9

Five overs went for 4, 6, 3, 12 and 5 runs. Mean: 6. What do the two sides add up to?

  • More below, since three overs sit below the mean
  • Six on each side
  • It needs the median to work out

Six weeks of rain totalled 90 mm, a mean of 15. One week is corrected up by 12 mm. What is the mean now?

  • 27 mm, because the mean follows the reading
  • 17 mm
  • 15 mm, since only one week changed

A stall's mean over five days is ₹620. A sixth day of ₹500 is added. Which way does the mean move?

  • Up, since ₹500 is a large amount
  • Down
  • Nowhere, since ₹500 is close to the rest

Four trays average 20 shoots, six trays average 30. What is the mean over all ten?

  • 25, halfway between 20 and 30
  • 26
  • 50, because 20 and 30 add to 50

One chart shows a tank's depth over four hours. One shows books under four kinds. Which may be joined?

  • Both — every reading is honest
  • The hourly one only
  • Neither — four dots are too few

A tank was read hourly: 200, 340, 460, 380, 200 litres. Only the first and last readings are kept and joined. What does that flat line show?

  • The tank stayed at 200 litres throughout
  • Only that both end readings were 200 litres
  • The tank must have been faulty

Two line graphs show bus seats 48, 50, 52 on three Mondays. One scale runs 0 to 56. The other runs 44 to 56. Which graph is misleading?

  • The one starting at 44 — a scale must start at zero
  • Neither, until the reader is told where the scale starts
  • The one starting at 0 — it hides a real rise

Your book's Part II, Chapter 5: Tales by Dots and Lines. You found a mean with a pencil and a ruler. Read the same tale in your book.

Next: Algebra Play. It has letters at work, identities you can check yourself.

Reveal every answer to finish this lesson.