2.3 Collecting Samples
Types of Samples
Random – occurring by chance
1) Simple Random Sampling
 All selections must have an equal chance of being chosen
 All combinations of selections must be equally likely
Example – How can you choose 3 people from the class?
>> put everybody’s name in a hat and draw 3 names
>> use a TI83+ calculator
Press MATH >>> PRB,
choose 5:randInt(start,end,quantity)
keep pressing ENTER for more choices
2) Systematic Random Sampling
 Used when sampling a fixed percent of the population
 Choose a random starting point and then you select every nth individual person for your
𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑧𝑒
study, where n is the sampling interval (found by evaluating 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒 )
Example – How can you choose 20% of the class?
>> do a simple random sampling for the starting point
23
23(0.2)
>> determine n {
=
23
4.6
= 5}
>> from the starting point, pick every 5th person
3) Stratified Random Sampling
 The population is divided into strata (groups based on age groups, geography, gender,
etc.)
 A simple random sample of the members is then taken
 The size of the sample for each stratum is proportionate to the stratum’s size
Example – How can you choose 8 members from the class so males and females are
fairly represented?
>> Calculate:
𝑇𝑜𝑡𝑎𝑙 𝑚𝑎𝑙𝑒𝑠
𝑇𝑜𝑡𝑎𝑙 𝑐𝑙𝑎𝑠𝑠
×8=
𝑇𝑜𝑡𝑎𝑙 𝑓𝑒𝑚𝑎𝑙𝑒𝑠
𝑇𝑜𝑡𝑎𝑙 𝑐𝑙𝑎𝑠𝑠
×8=
>> then do a simple random sample for each gender
4) Cluster Random Sampling
 Organize the population into groups (schools, communities, companies, etc.)
 Choose a random sample of the groups
 ALL members of the chosen group would be surveyed
Example – How can you choose people from the school to survey?
>> Do a random sample of all the homerooms for a particular grade using the master list
>> Then visit each homeroom and survey all members
5) Multi-Stage Random Sampling
 Organize the population into groups
 A random sample of the groups is chosen
 Then a random sample of the members of the chosen groups is taken
Example – How to pick 10% from the class?
>> Groups the students by row and pick 2 numbers from a hat that represent row
numbers
(2 out of 5 rows = 40% of the class)
>>Then pick 25% of the row randomly
(25% of 40% of the rows = 10% of the class)
6) Destructive Sampling
 Samples from which the selected elements cannot be reintroduced into the population
Example – light bulbs being tested for quality control – left on to burn until blown and
time of its life is recorded
Sample Size: How much is enough?
- Size of the population impacts the appropriate sample size
- Sample size is related to the reliability of the results
o Variability of the population
(greater variability = greater sample size)
o Amount of precision required for the study
o Sampling method chosen
“The larger the sample, the better the results!”
Homework: page 99 #1, 3, 5, 6, 8