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Counts and measures
1. Counts and measures
2. Counts and measures
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).
3. Integers
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.
4. Real number approximations
Real number approximations are approximations of measures.
Approximations usually include a certain number of significant digits.
0.3333...
0.6666...
1.0000...
3.1415...
5. Baseball counts and measures
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.
The
ERA (Earned Run Average) is more complicated.
6. Football
Is the number of yards gained by a running back or receiver in a play of American football a count or a measure?
7. American football
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?).
8. End of page