Counts and measures

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A count is an exact (nonnegative integer) number.
A measure is an approximation.

Example: 6 pack of Coke

You can count the number of bottles of Coke (i.e., six).
You measure how much is in each bottle (e.g., 12 ounces).

What is the difference between a count and a measure? Give a specific example that illustrates the difference.

Integers are positive and negative whole numbers that can be used for counts.

Math integers:

-∞, ..., -2, -1, 0, 1, 2, 3, ..., ∞

Computer integers:

-minInt, ..., -2, -1, 0, 1, 2, 3, ..., maxInt

For example, the minInt value for a signed byte is -128 while the maximum value is 128.

Real number approximations are approximations of measures.

Approximations usually include a certain number of significant digits.

0.3333... 0.6666... 1.0000... 3.1415...

When a baseball player gets 2 hits in 6 at bats, what is the batting average?

The number of hits, 2, and the number of at bats, 6, are counts.

The batting average is 2/6 = 0.333 = 33.3% which is a measure.

Is the number of yards gained by a running back or receiver in a play of American football a count or a measure?

Yes. A measure can be converted into a count.

For example, we measure distances. Now, the playing area of an American football field is 100 yards from goal-line to goal-line. What is the record for the longest possible run from scrimmage (that is, from goal-line to goal-line)? It is not 100 yards.

And it is not 99.9 yards.

Why? Even though the distance is measured by the officials on the field, football conventions dictate that, for record purposes, each ball placement is rounded off appropriately to the nearest yard. So the longest possible run is 99 yards. And for the players who have done such a run, it is a record that cannot be broken (why?).