# GCSE Statistics 6

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```					                                        Sampling Techniques

A manufacturer of matches needs to ensure that all his matches work - but to actually strike each
one would mean that he has none to sell - they have all been used. Therefore, he needs to have a
reliable method of sampling his stock.

The entire stock is known as the POPULATION, and the manufacturer obtains a
REPRESENTATIVE SAMPLE of his stock- i.e. the sample shows the “characteristics” of his
entire stock.

This representative sample cannot be limited in size, and every member of the population has to
have the same chance of being selected, and no part of the population is excluded. This is achieved
by RANDOM SAMPLING. Each member of the population is given a unique number. The
numbers are randomly selected, and then the members of the population relating to these numbers
are taken. These random numbers are either obtained from Random Number Tables or generated
from a calculator.

Types of Sampling

1. STRATIFIED SAMPLING
In this method samples are taken randomly from distinct groups of the data. These smaller samples
are in proportion to the size of the group, relative to the population. In a school, the whole school
represents the population, so the smaller samples would be taken from the year groups. A fixed
percentage or proportion of each year group could then be selected - i.e. 5% of each year group.

2. QUOTA SAMPLING
As before, samples are taken randomly from each group. This time, however, the target number or
quota is chosen from each of the group - irrespective of the size of each group. e.g. obtain 20 from
each age group/class etc.

3. CLUSTER SAMPLING
This applied to a large, widely spread population - e.g. a large sized town/county. Smaller areas of
the population (i.e. districts or council wards) are randomly selected. Within this cluster a random
sample is then chosen.

4. SYSTEMATIC SAMPLING
In this form of sampling, every member of the population has the same chance of being included,
but once the process starts, large sections of the population are excluded. It involves selecting every
nth person on a list.

For example, if the sample is to contain 20% of the population, then the systematic sampling would
involve selecting every 5th member of the population. This excludes four out of five members.

5. CONVENIENCE SAMPLING
In this type of sampling, the sample to be chosen is taken at one place and at one time. The sample
is then chosen from the population present.
Target Skills:- Sampling Techniques

1. State which of the following are subjective samples and which may be random samples.
a) A sample of patients chosen as participants in a drug test
b) The winners in a lottery
c) The top Year 10 mathematics set
d) Children whose surnames begin with the letter B

2. A partnership of G.P.’s would like to obtain a sample of patients on their register to investigate
their level of satisfaction with the management of the practice.

Discuss the problems they would face in simply assigning random numbers to each name on their
register.

3. A sample of 20 is to be taken from a school with 470 students.

Describe how you would use random numbers to select the sample.

4. It is required to sample the population of a certain town. Discuss the suitability of following
sampling frames:-
a) Names in the telephone directory
b) Names on the electoral roll
c) Membership of the local civic society

5. The principal of a college asks members of a Statistics class to suggest an appropriate sampling
method for seeking student opinion on the refurbishing of the main hall.
Proposal 1 Select every 20th student from an alphabetical list
Proposal 2 Select some students at random from each year group. and in proportion to the size of
each year group.
Proposal 3 Simply select students as they enter the dining hall
Proposal 4 Select students as they arrive at college, but ensure representative proportions with
respective to year and gender

In each case identify the sampling method and list its advantages and disadvantages. Which
proposal would you recommend ?

6. A school has 210 sixth formers, of which 30 do Arts Foundation courses, 80 do Science A Level
courses and the rest do Humanities.

a) Describe how you would obtain a 10% stratified sample.
b) Describe how you would obtain a stratified sample of size 50

7. A school has tickets for 48 students to go to an international art exhibition. There are 1200
students in the school, and the numbers in each year group are as follows:-
Year              7               8              9              10             11           12/13
Number            200             225            224            226            150            175

If the 48 are chosen from all 1200 students, describe how you would select a representative group
using:-
a) Pure random sampling
b) Stratified sampling
c) Quota sampling
State which of these methods is the most appropriate.

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