Track quiz

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
Idea	How it goes
Balance point	The mean is the one point where readings balance.
The two sides	Distances above the mean total the same as below.
A moved reading	The mean moves by the move, shared among the readings.
A new reading	Above the mean it pulls up, below it pulls down.
Two groups	Rebuild both totals, add them, then share by the total count.
Equal groups	Two means average to the true mean when the counts match.
Joining dots	Join dots when the bottom scale has a real order.
The side scale	Where 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.

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