- Statistics are numbers ("descriptive statistics")
First Definition of Statistics: Statistics are numbers
calculated from a collection of data
"Data": items of information, either numerical or non-numerical
(quantitative versus qualitative)
Examples of statistics:
- baseball "averages"
- percent, proportion of NKU students that graduated from the same high
school as one of their parents
- average height of NKU students
- percentages of students preferring each type of soft drinks offered on NKU
campus
- Statistics is a science ("inferential statistics")
Second Definition of Statistics: Statistics is a science
that deals with the collection and summary of information that
is then used to make interpretations, decisions, estimates,
predictions, etc.
Examples:
- Let's try some inferential statistics. Inferential Statistics
is tied up with probability. We may hear someone make a statement,
and then we say "Nonsense!", or "That seems reasonable...."
But we may want to do more: we may want to test an assertion, to
see what we can detect or infer from our examination of the
data. And for that we'll need probabilities.
Here's a simple probability example:
- What's the probability of a 5 appearing on a throw of a
die?
- What's the probability of an odd number appearing?
Here's another:
- How do we determine if a coin is fair?
- (Can we determine if a coin is fair in a single toss?)
(Of course we must always be on the lookout for anything funky about
the setup.)
Example: So let's think about those NKU student heights:
- What's the probability that the class average height is above 7 feet?
- What's the probability that the class average height is below 7 feet?
- As we shift the "7 feet" part around, how will these probabilities
change? In particular, begin dropping the 7 towards 4, and what would
you see happening to the intuitive probabilities?
Let's think about how we might graph our intuition.
- Now let's figure out how we'd test some assertions:
- Suppose I assert that everyone in class is 6 feet tall.
- What could we do to test this assertion?
- In particular, why don't we generally need to know the
height of everyone in class?
- What could we do to test these assertions (without simply
calculating the mean for the class! We're trying to be
clever....)?
- Suppose I assert that the mean (or average) height
is 6.
- Suppose I assert that the mean (or average) height
for men is greater than that for women.
Another example: Average ("mean") temperature in Cincinnati:
- What statistics are being shown in this graphic?
- How do we relate the statistics to probabilities?
- The high is forecast to be 41 degrees F on Thursday. How
do you relate that to probabilities for this particular
date?
- On Sunday, the high is forecast to be 15 degrees F. How do
you relate that to probabilities for this particular
date?
- This example illustrates distributions of numbers,
rather than just a single number. Distributions will be very
important in this course.