Understanding Sampling Interval in Systematic Sampling

In research, when we want to study a large group of people or items (called a population), we often pick a smaller group to represent them. This smaller group is called a sample. Systematic sampling is one way to select this sample.

Systematic sampling involves selecting elements from an ordered sampling frame at a regular interval. This regular interval is known as the sampling interval.

Key Concepts and Formula for Sampling Interval

To calculate the sampling interval, we need two main pieces of information:

• Accessible Population (N): This is the total number of individuals or items available for sampling.
• Sample Size (n): This is the number of individuals or items you want to select for your sample.

The formula to calculate the sampling interval (\(k\)) is:

\[k = \frac{\text{Accessible Population (N)}}{\text{Sample Size (n)}}\]

Or simply:

\[k = \frac{N}{n}\]

Calculating the Sampling Interval

Let's apply the formula to the given problem:

• Accessible Population (N) = 40,000
• Sample Size (n) = 200

Now, we will substitute these values into the formula for the sampling interval:

\[k = \frac{40,000}{200}\]

To perform the division, we can simplify by cancelling zeros:

\[k = \frac{400}{2}\]

Then, divide 400 by 2:

\[k = 200\]

Sampling Interval Result

The calculated sampling interval is 200. This means that if you were to use systematic sampling, you would select every 200th element from your ordered accessible population list after selecting a random starting point. This ensures a systematic and representative sample from the given accessible population based on the sample size.

Therefore, the sampling interval is 200.