- Midterm Practice Problems Today!
Practice Midterm:
Q1: Describe this distribution.
Q2: Statistic or Parameter
Q3: Probability
Describe this distribution
Use the checklist:
Center:
where is the middle, if applicable
Spread: how far from the middle does data go?
Shape: modes, skew, known limits (positive only?)
Outliers: notable values away from most data
Shape: Can’t tell number of modes from boxplot.
Spread:
Extra page for work or notes
Extra page for work or notes
Here is a histogram of that same data. Be prepared for both.
Could you make similar observations from this?
Statistic, or Parameter?
Statistics are pieces of information about Samples. Samples
are a small group that we measure because we can afford to.
We hope that the sample is a good representation of what we
really want information about, which is the population.
Parameters are pieces of information about the Population.
Is this a statistic or a parameter? What’s the population or interest?
If there’s a sample, what is it?
“Plastic bag use has shrunk 59 per
cent across the province
since the industry agreed to voluntary targets, the grocers note.”
Plastic bag ban: Who loses – Toronto Star June 7, 2012
Statistic or Parameter.
42% of the yes/no responses in a voluntary online poll
responded in favour of a ban on plastic bags.
This is a ____________
Also, this is _____________________. Because the
sample was of anyone who volunteered their opinion, not a
randomly selected group.
Parameter or statistic?
“According to a poll released Tuesday, nearly 20 percent of
U.S. citizens now believe Barack Obama is a cactus”
- Poll: 1 in 5 Americans Believe Obama is a Cactus. The Onion. Sep. 20, 2010.
This is a:
The sample is:
The population is:
Probability: Three rules.
Converse rule:
This is always true.
Related: Probabilities can only be from 0 to 1.
Multiplication rule
Pr(A and B) = Pr(A) x Pr(B)
This is only true when events are independent. That means
they don’t affect each other.
Another perspective: Two things are independent if knowing
one doesn’t tell you anything about the other.
Addition Rule
Pr(A OR B) = Pr(A) + Pr(B)
This only works when A and B cannot happen together,
otherwise known as mutually exclusive, because one
happening excludes the other from happening.
Let’s roll!
Consider two six-sided dice, a WHITE die and a RED die.
What is the probability that the white die rolls a 1 or 2?
Let’s roll!
Consider two six-sided dice, a WHITE die and a RED die.
What is the probability that the white die rolls a 1 or 2?
Two faces out of six possible faces.
What is the probability that white rolls 1 or 2 AND that red
rolls 2,3,or 4?
Pr(White rolls 1 or 2) =
Pr(Red rolls 2,3, or 4) =
Pr(W12 AND R234) =
Can we use the multiplication rule to find
Pr(White is 1 or 2 AND Red higher than White) ?
Knowing that White is a low number like 1 or 2 changes the
chances of Red rolling higher than White, so we can’t use the
multiplication rule.
These events are NOT INDEPENDENT. (See 2d in Assn2 answer
key)
Don’t wear yourself out before Monday.
Be like this,
not like this