The concept of margin of error is a key statistical tool that helps us understand the degree of uncertainty associated with the results of a survey. Essentially, the margin of error provides an estimate of how close the results from a sample survey are likely to be to the results that would have been obtained if the entire population had been surveyed. In more technical terms, the margin of error is calculated by multiplying the critical value by the standard deviation.
In statistical terms, the margin of error is usually represented by E and can be calculated using the following formula:
where,
n= size of the sample
σ= Standard Deviation of the Population
z = z score (standard deviation units)
Examples to Illustrate the Concept
Example: Suppose a random sample of 40 employees has an average monthly income of 3500 with a standard deviation of 500. Calculate the margin of error for a confidence level of 0.90?
Solution:
Given
n=40, Standard Deviation= 500
σ = 500
Confidence level = 0.90
For a 90% confidence level, z = 1.645
Margin of error = z × σ/√n
= 1.645 × 500/√40
= 1.645 × 79.06
= 130.06
= 130 (approximately)