Transcript Random Sampling

1) Find a distribution of 5 positive whole numbers with
the following properties:
a) Mean = 4
b) Median = 3
c) Mode = 3
2) How many distributions can you find with these same
properties?
3) What is the maximum range of the distribution?
4) Find the distribution of 5 positive whole numbers with
a mean = 31, median = 33, Mode = 34, Range = 8
Math I
UNIT QUESTION: How do you use
probability to make plans and predict
for the future?
Standard: MM1D1-3
Today’s Question:
How do we take a random sample,
and what statistics can we find with
the data?
Standard: MM1D3.a.
Data consists of information coming from observations, counts,
measurement, or responses. The singular of data is datum.
Statistics is the science of collecting, organizing, analyzing, and
interpreting data in order to make decisions.
A population is the collection of all outcomes, responses,
measurements, or count that are of interest
A sample is a subset of a population
A parameter is a numerical description of a population characteristic.
A statistic is numerical description of a sample characteristic
Population Parameter
Sample Statistic
Give some examples of why we would want to use data from a
sample instead of looking at the whole population
Sampling can be less expensive
Sampling can be used to make predictions of things that have not
happened yet – think of polls in an election
Sometimes the sample is destroyed. Think of bombs or destructive
testing of engineering materials. If we were to sample the whole
population, it would all be destroyed.
Reason:
Easy and less expensive
Problems with non-statisical sampling is that the results can be
misleading.
A voluntary sample is made up of people who self-select into the
survey. Often, these folks have a strong interest in the main
topic of the survey. Give some examples.
A convenience sample is made up of people who are easy to
reach. Give some examples.
Simple Random Sampling (SRS): All data points have an equal
chance of being selected. We will be using this one the most.
Other common types of sampling include:
1.
Census – count the whole population
2. Stratified sampling – cut the population into parts (strata)
and then select sample randomly from each part
3. Cluster sampling – cut the population into parts (clusters),
then sample all points within the selected clusters
4. Systematic random sampling – sample every nth data point
A biased sample is a sample that is
not representative of the population.
A representative sample is a sample
that accurately reflects the
characteristics of the population.
Some Causes of Bias
• Undercoverage. Undercoverage occurs when some
members of the population are inadequately represented in
the sample.
• A classic example of undercoverage is the Literary Digest
voter survey, which predicted that Alfred Landon would
beat Franklin Roosevelt in the 1936 presidential election.
• The survey relied on a convenience sample, drawn from
telephone directories and car registration lists. In 1936,
people who owned cars and telephones tended to be more
affluent. Undercoverage is often a problem with
convenience samples.
• The survey sample suffered from undercoverage of lowincome voters, who tended to be Democrats.
Some Causes of Bias
• Nonresponse bias. Sometimes, individuals
chosen for the sample are unwilling or
unable to participate in the survey.
Some Causes of Bias
• Voluntary response bias occurs when
sample members are self-selected
volunteers.
• An example would be call-in radio shows
that solicit audience participation in surveys
on controversial topics (abortion,
affirmative action, gun control, etc.). The
resulting sample tends to overrepresent
individuals who have strong opinions.
Some Causes of Bias
• Leading questions. The wording of the
question may be loaded in some way to
unduly favor one response over another.
• Example: Would you favor raising taxes to
help feed our starving children?
• Example: You like my outfit, don’t you?
Some Causes of Bias
• Social desirability. Most people like to
present themselves in a favorable light, so
they will be reluctant to admit to unsavory
attitudes or illegal activities in a survey,
particularly if survey results are not
confidential.
• Example: How many times have you done
drugs in the past 30 days?
• Example: How many times have you kicked
your baby brother this week?
John surveys every fifth person leaving a pet supply store. Of those
surveyed, ¾ support the city manager’s proposition to tear down the
old library and replace the area with the construction of a new pet
park. John plans to write a letter to the editor of the local newspaper
about the proposal for the new pet park stating that there is
tremendous support from the citizens of the town for constructing a
new pet park.
a) Can the conclusion John stated be accurately supported?
b) Suggest another plan for obtaining a good sample population.
We want to know the average height of students at Salem High
School.
What would be a good method to find this number without checking
every student?
Sample Problem #1:
Your school is conducting a survey on a proposed dress code. The
first 20 students entering the school in the morning are surveyed.
What type of sampling method is used?
a)
b)
c)
d)
Convenience
Random
Stratified random
Systematic
What could be done to help reduce (notice I did not say eliminate)
bias and make the survey a better random sample?
Sample Problem #2:
A principal is surveying the parents of his school to find out if they
support extending the school day by 20 minutes. Which of the
following methods of choosing a sample will most likely result in a
sample that is representative of all parents?
a) Surveying all the parents at a parent – teacher meeting
b) Surveying 50 parents of 9th grade students
c) Surveying all the parents who volunteer for a school fundraiser
d) Selecting every 20th name from an alphabetical list of all parents
and surveying those parents.
Sample Problem #3:
Explain why the following questions are biased or not:
a) Do you prefer creamy macaroni and cheese or bland rice?
b) Don’t you feel the city is wasting money by building that new
stadium?
c) Do you prefer shopping online or in the stores?
d)Don’t you agree that the driving age should be raised to 18 to
decrease the number of accidents?
Summary Statistics
• We go to all the bother to generate unbiased sampling to generate representative
samples.
• Representative samples provide summary
statistics that can be used to predict what
will happen in the population.
Use Sample Statistics to Predict
Population Behavior
Sample Problem 1:
What is the probability of having three
children, the first two being male, and the
third female?
0.5 * 0.5 * 0.5 = 0.125
Use Sample Statistics to Predict
Population Behavior
Sample Problem 2:
The Chicken Clucker Egg Farm has done a
random sample and has determined that on
the average, one egg per dozen is cracked.
What is the probability that any egg in the
farm will be cracked?
1/12 = 0.08
Use Sample Statistics to Predict
Population Behavior
Sample Problem 3:
Kareem Abdul-Jabbar had a 0.739 free throw
average in the 1988/89 season. Based on
these statistics, how many free throws
would he make in 7 attempts?
7 * 0.739 = 5.2, or 5 free throws
Work
• Page 361, # 1 – 11all
• Finish the warm-up for extra credit
Other Work
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Quiz Tuesday
Test Friday
Match bar chart to box and whisker plot
Algebra
Worksheets from Frameworks
5 number summary worksheet
Presidential data – box plots – box and
whisker plots