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Pioneer Junior College

H2 MathematicsTutorial 26: SamPling Methods

ire collection of data we want to study'

Common sampling methods include

o SimpleRandomSamPlingo Stratitied Sampling

o Systemntic Sampling

o Quota Sampling

Questions for discussions

l. Give a reason why, in carrying out a statistical investigation, a sample rather than a complete

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In the Arts cohort of 140 students this year, there are 60 girls and 80 boys. A survey is to be

taken to find methods to improve the college's canteen services. A sample of 14 members of

this group is needed for the survey.

The college decides to use one of the following methods to obtain the names of students for the

sample:

A: Every 10ft name on the Arts register is selected for the sample.

B: Each- of the 140 names is allocated a different number from 1 to 140 inclusive; the

college's computer then picks 14 different random numbers between 1 and 140 inclusive.

(i) State briefly one advantage and one disadvantage for each method. Il]iiq nescrtbe how method B ian be modified to give a stratified random sample. t21

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In a small school there are 3 classes, each of 30 children, and2 classes, each of 20 children. A

stirdent takes a sample of 10 children from the school, by taking 2 children at random from

each class. State, *ith u reason, whether this gives a random sample of 10 children from the

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e certiih drivate estate cbntains many small houses (with small gardens) and a few large

houses (with large gardens). A sample survey of all houses is to be carried out in this estate. A

student suggests-that the sample"outd

be selected by sticking a pin into a map of the estate the

requisite number of times, while blindfolded.

(i) Give two reasons wtry this method does not produce a random sample. t2l

iiil oescribe a better method. t21

[2006 Specimen Paper HllH2 Example 1]

5. (i) Give a real-life example of a situation in which quota sampling could be used- 9"-p19"why quota sampling would be appropriate in this situation, and describe briefly any

disadvantage tfrat q"ota sampting has. t4l

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Explain briefly whether it would be possible to use stratified sampling in the situation you

have described inpart (i). tU[N07/IV5l

has a canteen where students can buy their lunch. Each day most, but not all, students

their lunch in the canteen.

headteacher wants to find out what students think of the lunches provided in the canteen.

one particular day she selects a sample of students to interview from those buying their

by

. choosing at random one of the first 10 students to buy their lunch,

o then choosing every 10th student after the first student chosen.

What is this type of sampling method calted? tllState one advantage andone disadvantage of the sampling method usgd in this context. [2]

n6rribe an alteniative sampling method which would be better in this case. t21

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has 950 pupils. A sample of 50 pupils is to be chosen to take part in a survey.

how the tutnil. could be chosen using systematic sampling l2lpurpose of the gr*"y is to investigate pupils' opinions about the sports facilities available

school. Give a r"*ot why a stratifiedsampte might be preferable in this context. I2llH2lr{O8/IV5l

insurance compaoy receives a large number of claims for flood damage. on a particular day

receives 72 such claims. Because of staff shortages, it is only possible to process

these claims.

Describe how you would choose a systematic random sample of size 8 from the received

claims. I21

Comment on whether this method of sampling gives a better indication of the value of the

72 claims as compared to simply choosing as the sample the first 8 claims received. tUlHlA{09/1l(a)l

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1.

4(i)

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Suggested Answers for Discussion Questions

l. Cheaper/ less time consuming/ any other legit reason.

2(i) Method A: Systematic sampling.

lt is easy to conduct since the college has a register of all the students. Since the register isarranged in alphabetical order, we cannot ensure the gender ratio is maintained. We may endup having a lot more girls than boys in the sample, where the gender ratio is very skewed.Method B: Simple random sampling.lt is free from bias. The register must be complete and up-to-date. Cannot ensure gender ratio.Therefore simple random sampling would be cumbersome if the population is large.

2(ii) Each of the 60 girls'names is allocated a different number from Gl to G60 inclusive, and eachof the 80 boys'names is allocated a different number from Bl to 880 inclusive. The college'scomputer then picks 6 different random numbers between Gl and G60 inclusive and 8

different random numbers between Bl and B80 inclusive.

No, this procedure does not give a random sample. The probability of a sample of size 2 being

chosen in the classes of 30 students is *f , while the probability of a sample of size 2 beingL)

chosen in the classes of 20 students is * Therefore not all samples of size 2 haveequaltuc,

chance ofbeing chosen.

Large houses with large garden may have a bigger area shown"on the map than small houseswith small gardens. Then, the probability of a large house being selected is higher than that of

small houses.

Since the student needs to know the boundary (or area) where he can stick his pin, by stickingthe pin more to the right of the map, he is selecting the houses on the eastern side of the estate.Hence there is bias.

4(ii) Stratified random sampling - The ratio of number of small houses to large houses in the sampleshould reflect the ratio of small houses to large houses in the estate. Within each strata, theunit'number of each house can be written on i regular sized piece of paper and placed in a box.

The papers are then thoroughly mixed and the required number of houses for the survey is then

randomly picked out by the student.

Simple random sampling is possible here but stratified sampling is preferred.

5(i) Students are given a short time frame of 2 days to gather feedback on whether their school has

a positive image among the general public. Since time is limited, quota sampling where theygather feedback from 100 people at the nearest MRT station would be appropriate.

A disadvantage would be that only the opinion of people staying around the MRT stationwould be captured. (Bias because of geographical location)

5(ii) It is possible to use stratified sampling by gathering opinion of the different age group ofpeople because the different age groups may look out for different things.