3-6
6th grade math
Sampling Methods
Objective
• To understand how the method of sampling determines
how representative the sample is of the population.
• Why? To understand that the sample selected to study
must represent the population being investigated if
inferences about the population are to be valid. The best
way to choose a sample is randomly. A random sample is
usually a good representation of the population you are
drawing from. But contacting all members of the sample
might not be possible. Many methods of gathering data
have some bias. Paper surveys may not reflect those who
are too busy to reply or who have no interest in the topic
of the survey.
California State Standards
SDP 2.2 : Identify different ways of selecting a
sample (e.g., convenience sampling, responses to
a survey, random sampling) and which method
makes a sample more representative for a
population.
SDP 2.4
: Identify data that represent sampling
errors and explain why the sample (and the
display) might be biased.
Vocabulary
• Random Sampling
– A sampling method in which each person or thing
has an equal chance of being chosen
• Asking people off the street
• Representative
– A random sampling which is a good match for the
population
• Asking people at a doctor’s office about taking
medicines, in general
• (RR) = Random and Representative!!
• Biased
More Vocabulary…
– A sample which does not mirror the population
• Asking people at a doctor’s office about taking a specific
medicine, especially if the type of medicine ≈ the type of doctor
• Convenience Sampling
– A sampling method where any convenient method is
used to choose the sample
• Asking people at a doctor’s office about taking a specific
medicine, especially if the type of medicine ≈ the type of doctor
• Responses to a Survey
– A form to fill out (asking sampling questions) is usually
biased
• Fill out a form-survey about your car buying experience
• (BCRS) = Bias is Convenient and Responding to a
Survey
How to Work with Sampling Methods
1) Randomly choose an ‘X’
number samples.
2) Find mean, median,
mode. Are they similar,
statistically?
3) Identify the sample
being used, and does it
represent the
population being
studied? Was there
bias?
1) Choose any 10.
36, 53, 127, 176, 180, 284, 304, 311, 426, 608
2) Mean = 2329/10 = 232.9
≈ 233
Median = 180 + 284 =
464/2 = 232
Mode = none
Yes statistically similar.
3) Sample = Number of
districts in states
Not bias because it was
random. (RR)
How to Work with Sampling Methods
1) Randomly choose an ‘X’
number samples.
2) Find mean, median,
mode. Are they similar,
statistically?
3) Identify the sample being
used, and does it
represent the population
being studied? Was
there bias?
1) Choose top 10.
67, 180, 501, 608, 661, 674, 705, 929, 994, 1042
2) Mean = 6361/10 = 636.1
≈ 636
Median = 661 + 674 =
1335/2 = 667.5 ≈ 668
Mode = none
Not statistically similar.
3) Sample = Number of districts
in states
Yes, biased because it was
conveniently chosen.
(BCRS)
How to Work with Sampling Methods
1) Randomly choose an
‘X’ number samples.
2) Find mean, median,
mode. Are they similar,
statistically?
3) Identify the sample
being used, and does it
represent the
population being
studied? Was there
bias?
1) 10 people responded to a
written survey: pairs of
shoes.
1, 3, 5, 5, 6, 6, 6, 7, 8, 12
2) Mean = 59/10 = 5.9
≈6
Median = 6
Mode = 6
Yes, statistically similar.
3) Sample = pairs of shoes
Yes, biased because it was
conveniently chosen.
(BCRS)
Try It!
A. Tell whether each sample is
representative (RR) or biased
(BCRS).
B. Identify if: random sampling,
convenience sampling, or
responses to a survey.
1) Mailing questionnaire to
all eligible voters. 12%
respond and return the
form.
2) Principal questions every
student whose locker
number ends in a 9 to
gather student input
about plans for a new
library.
1) A. Biased
B. Responses to a survey
(BCRS)
2) A. Representative
B. Random sampling (RR)
Objective Review
• To understand how the method of sampling determines how
representative the sample is of the population.
• Why? You now understand that the sample selected to study must
represent the population being investigated if inferences about the
population are to be valid. You know that the best way to choose a
sample is randomly. A random sample is usually a good
representation of the population you are drawing from. Understand
that contacting all members of the sample might not be possible. You
also know that many methods of gathering data have some bias.
Paper surveys may not reflect those who are too busy to reply or who
have no interest in the topic of the survey.
Independent Practice
• Complete problems 3-5
• You may work with a
partner to discuss the
answers.
• For extra points, write
the reasons for your
answers.
• If time, complete Mixed
Review: 6-9
• If still more time, work
on Accelerated Math.