### Statistics - sampling methods

#### Sample

certain cereal manufacturer wants to carry out a survey in the county Middlesex to determine the most popular breakfast cereal among school kids. Asking each and every child about their choice is next to impossible; the number of kids runs into millions.

It is what we call in statistics, a vast **population.** When we
are faced with a situation of this kind, it makes sense to concentrate on a
manageable group of kids to get a true picture of their needs.

This small group
is called a **sample** and the
process is known as **sampling.**

We must
be very careful about this small group of individuals – sample.

At the very
beginning it must fulfil the following requirements:

- The sample must be small enough to manage
- The sample must be large enough to represent the views of the whole population – in this case all the kids in the county Middlesex
- When picking up individuals, bias should be avoided – skin colour, race, religion, personal views of the interviewer towards the individuals to be selected. In other words, we must ensure that each member of the population has an equal chance of being selected.

With setting our sight on these points, the next task is to number the whole population in a certain way; the letters of the first names and surnames can be considered in this numbering process. Each and every member of the population now has a number.

The
**size** of the sample is normally between **5%-10% of the population**.

**E.g.**

The population – in this case the kids in Heathfield Grammar School – are numbered in the following way:

- Adam Ashford
- Adrian Burton
- Ajit Bra
- Balvinder Chopra
- Azis
- Hamza
- ...
- ...
- Melani Yanks
- Nigel Zamir
- Owen Bright
- ...
- ...
- Raymond Hill
- Tim Sinclair

Now we have to choose 60 members from the above list. It is the process of sampling. This can be done in three different ways:

**Random sampling****Stratified sampling****Selective sampling**

#### Random Sampling

Generate 60 random numbers by any of the following methods:

- A calculator - Press the
**‘Ran#‘**button on the calculator and a number will appear on the screen. Take the first three digits, if they represent a number less than 600 - E.g. if the random number is 0.59824421, take 598 and choose the student with that number for the sample. - Using a simple programme - Press the button to get 60 random numbers:
- Using three spinners:

Throw the three spinners and take the number on display in order – 599, 400, 398 etc. Spin all three 60 times. You can get sixty random numbers by any one of these three methods. It is random sampling.

#### Stratified Sampling

In this method, we divide the population into smaller units: we can divide them on the basis of ethnicity of the members – just one way of grouping the population. Then the members for the sample are chosen from these individuals, of course in proportion to the size of each unit.

**E.g.**

The population of Heathfield Grammar School is grouped in the following way:

White Caucasians | 150 |

Sikhs | 180 |

Muslims | 120 |

Afro-Caribbean | 90 |

Other | 60 |

The members for the sample in proportion to the size of the groups are chosen as follows:

White Caucasians | 10% of 150 = 15 |

Sikhs | 10% of 180 = 18 |

Muslims | 10% of 120 = 12 |

Afro-Caribbean | 10% of 90 = 9 |

Other | 10% of 60 = 6 |

Total | 60 |

How do you choose these members from each group? You can use random sampling for that purpose.

#### Selective Sampling

In this method, a random number is generated by some means – calculator, spinner or a simple computer programme.

If the number turns out to be **5**, then every **5 ^{th}** member must be picked up for the sample.