Sampling Introduction
Since it is usually not practical to test every item in a production run, we rely on samples. To have meaning the samples must be representative of the population from which they come. A representative sample reflects the nature of the population from which it is drawn. A sample which has been chosen at random will reflect the population, and will vary in a predictable way. If a sample is not representative, it is biased. In all sampling it is extremely important to avoid bias.

Some examples of sampling methods. Which are likely to be biased, and how?

1. A radio station takes a survey about gun control by asking listeners to call in.

2. An inspector measures the first ten castings of each day's run.

3. Tacos are checked for weight at every order number that ends in 25.

4. Tacos are checked for weight at random intervals according to the manager.

5. Electrical components from batches of 1000 are to be tested. To choose which component is tested, a technician generates 3-digit random numbers on a calculator.

Answers

Remarks

Example 4 is called a judgment sample. If the manager in #4 says he picked at random when he chose by picking haphazardly, did he really pick at random? For an unbiased sample each taco must have an equal chance of being picked. The manager's eye may have been attracted to certain ones. The manager could be choosing at only one time of day (when business was slow). Patterns in his choice may have introduced a bias in the sampling process.

Example 5 illustrates a random sample. A random sample is chosen using mathematically random methods to pick the sample. In a random sample each member of the population has an equal chance of being chosen. "Random" in statistics does not mean haphazard or any method of individual choice. Random methods include rolling a die, picking number from a hat, or using a list of random numbers. Computers and calculators can generate numbers random enough for most uses. The distribution of random numbers should be uniform.

Using random numbers to pick samples free from bias. A technician wants to choose parts for testing. Here are 50 three-digit random numbers generated by a calculator with a random number generator. Using these random numbers, the technician picks item number 318 from the first batch, number 758 from the second batch, and so on.

.318 .758 .012 .301 .360 .968 .950 .758 .510 .915
.675 .961 .040 .369 .516 .311 .673 .167 .294 .022
.290 .656 .284 .906 .330 .967 .078 .696 .075 .881
.359 .054 .330 .068 .724 .530 .723 .976 .922 .150
.809 .556 .814 .676 .932 .152 .427 .300 .573 .040

The button below runs a program to generate a random number between 1 and 100.

The following sampling activity compares judgmental and random sampling.

On the next page you will look at a page with 100 "viruses" of different sizes. Each virus is made up of 1 to 12 units and each "virus" is numbered in red for identification.
Your goal will be to estimate the average size of all 100 viruses.

Don't look at the page yet! Before you open the virus page here is a preview.

The size of virus number 7 is 3. Number 30 has a size of 6.
What is the size of number 95?

The average size of all three is (3+6+6 )/ 3 = 15/3 = 5 units

I'm ready! Go to virus page