Mathematics in Daily Life Data for Decisions

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Mathematics in Daily LifeData for Decisions 

• 
  POON TENG HIN

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Introduction
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Critical thinking

• When we are reading articles or making decisions,
  we need to ask
• What is the statements?
• What is the conclusion/decision?
• What are the reasons for supporting the
• Conclusion/decision?

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Data as reason

• One of the effective reasons to support a
  conclusion is Data.

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More examples
Consumer survey
Marketing Plan
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Sampling
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Sampling

• Demo ?

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Sampling methods
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Sampling Methods

• Non Probability sampling
• Does not involve random selection
• Probability sampling
• Involve random selection

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For your reference(explanation from web)

• Purposive Sampling Select particular group of
  people. The accuracy depends on how to select.
• Accidental sampling involves the sample being
  drawn from that part of the population which is
  close to hand. That is, a sample population
  selected because it is readily available and
  convenient.
• Quota sampling means the population is first
  segmented into mutually exclusive sub-groups and
  select samples in each sub-group with a quota.
• Convenience sampling the researcher uses
  subjects that are easy to reach.
• Snowball sampling existing samples recruit
  future sample from among their acquaintances.
  Thus the sample group appears to grow like a
  rolling snowball.

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For your reference(explanation from web)

• Simple random sample each unit of the
  population has an equal chance of being selected
  for the sample.
•   System Random Sampling starting point is
  chosen at random, and thereafter take sample at
  regular intervals. 
•   Stratified Random Sampling process of
  dividing members of the population into
  homogeneous subgroups before sampling. Then
  random or systematic sampling is applied within
  each stratum.
•   Cluster Sampling the total population is
  divided into these groups (or clusters) and
  a sample of the groups is selected. Then the
  samples are collected from the elements within
  each selected group.
• Multi-Stage Sampling First stage is
  cluster sampling, then randomly selects elements
  from each cluster.

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Non Probability sampling
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Login
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E.G I have been invited in a event
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Which sampling method does it involved?
Purposive Sampling Accidental
Sampling Quota Sampling
Convenience sampling
Topic Compare the motivation of leisure
activities between working people and people in
school
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Snowball sampling
If the people attended in the event can invite
their friends into it, then it is a kind of
Snowball Sampling
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Voluntary response sample
When participants could choose to participate or
not. This causes some bias.
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Response rate
However, Some people do not attend..
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Response rate

• Response rate
• (Respondents / Sample size) X 100

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How response rate effect the result?

• If the response rate are low
• E.g. Sample size 100, response rate 40
• Result Agree 25 (most
  people agree)
• Disagree15
• Non attended Agree 25
• Disagree35 (most
  people disagree)
• Total Agree 50 (Different
  results)
• Disagree50

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Response Bias

• If response rate is low, the accuracy of the
  sampling will decrease.
• We should aware of the response rate when we make
  decision.

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Non Probability sampling
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Simple Random Sampling

• Each unit of the population has an equal chance
  of being selected for the sample.
• Methods
• Drawing
• Table of random numbers
• Computer programs

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Table of random numbers
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Use the table

• Decide how large a number you need before.
• Decide how to across the page. To the right, to
  the right, down the page or up the page.

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E.G If we marked 100 tigers, and fond 2
marked tigers in 60 afterward so
2/60 100/N
N 3000 3000 tigers in the area.
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How can the conclusion be affected?

• Tigers are live animal, we cannot control it.
• Marked tiger may die, or be alertness.
• Non Living may get better accuracy.

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Conclusion

• Should aware of the choosing of sampling methods
  and understand how a survey conducted before
  believe in it.

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Homework

• Suggest a process using simple random sampling to
  determine the height of UST students
• 2. If I marked 200 fish and released them in the
  pool, after 2 days, I catch 200 fish and there
  are 40 of them are marked. What is the population
  of the fish in the pool? What factors may affect
  the result?
• Extra credit What factors will affect the
  sample size?

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End