Random sampling

A method of sampling a population using an equal chance of being selected.

Random sampling means that each has the same chance of being selected.

Random sampling is where random people are chosen to be sampled but all have an equal chance of being picked

Random number generators are used in the lottery.

Equal chances of picking out a sample of, say, people from a population can be like picking a number out of a hat, giving you a random result.

Picking a number out of a hat is random

Random sampling is like the lottery where each ball has an equal chance of being selected

The lottery is a random selection of numbers.

A computer can randomly generate numbers, this is the most reliable way of generating randomly

A computer can generate numbers randomly.

Example 1

The grouped frequency table shows information about the weights, in kilograms, of 20 students, chosen at random from Year 11.

An example of random sampling

There are 300 students in Year 11. Work out an estimate for the number of students in Year 11 whose weight is between 50 kg and 60 kg.

Answer:

`300=20` (100% of the sample)

`x=7`

(see our section on percentages)

`300/x=20/7`

Therefore `x=(300times7)/20`

`x=105`

Answer:

There are approximately 105 students in year 11 between 50kg and 60kg.

Example 2

Explain how a simple random sample can be taken from all the people using a library in a day.

Answer:

E.g. Interview every 20th person coming out of the library throughout the day.