Informal Geometry Period 1

1
Warm Up

• Find a distribution of 5 positive whole numbers
  with the following properties
• Mean 4
• Median 3
• Mode 3
• How many distributions can you find with these
  same properties?
• What is the maximum range of the distribution?
• Find the distribution of 5 positive whole numbers
  with a mean 31, median 33, Mode 34, Range
  8

2
Math I
UNIT QUESTION How do you use probability to make
plans and predict for the future? Standard
MM1D1-3 Todays Question How do we take a
random sample, and what statistics can we find
with the data? Standard MM1D3.a.
3
Vocabulary
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
4
Sampling
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.
5
Non Statistical Types of Sampling
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.
6
Statistical Sampling

• 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
• Census count the whole population
• Stratified sampling cut the population into
  parts (strata) and then select sample randomly
  from each part
• Cluster sampling cut the population into parts
  (clusters), then sample all points within the
  selected clusters
• Systematic random sampling sample every nth
  data point

7
Bias
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.
8
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
  low-income voters, who tended to be Democrats.

9
Some Causes of Bias

• Nonresponse bias. Sometimes, individuals chosen
  for the sample are unwilling or unable to
  participate in the survey.

10
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.

11
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, dont you?

12
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?

13
Random Sampling

• John surveys every fifth person leaving a pet
  supply store. Of those surveyed, ¾ support the
  city managers 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.
• Can the conclusion John stated be accurately
  supported?
• b) Suggest another plan for obtaining a good
  sample population.

14
Random Sampling
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?
15
Random Sampling

• 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?
• 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?

16
Random Sampling

• 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?
• Surveying all the parents at a parent teacher
  meeting
• Surveying 50 parents of 9th grade students
• Surveying all the parents who volunteer for a
  school fundraiser
• Selecting every 20th name from an alphabetical
  list of all parents and surveying those parents.

17
Random Sampling

• Sample Problem 3
• Explain why the following questions are biased
  or not
• Do you prefer creamy macaroni and cheese or
  bland rice?
• Dont you feel the city is wasting money by
  building that new stadium?
• Do you prefer shopping online or in the stores?
• Dont you agree that the driving age should be
  raised to 18 to decrease the number of accidents?

18
Summary Statistics

• We go to all the bother to generate un-biased
  sampling to generate representative samples.
• Representative samples provide summary statistics
  that can be used to predict what will happen in
  the population.

19
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

20
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

21
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

22
Work

• Page 361, 1 11all
• Finish the warm-up for extra credit

23
Other Work

• 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