# Margin of Error Formula

The margin of error is a statistic expressing an amount of random sampling error in a survey’s results. It asserts a likelihood that the result from a sample is close to the number one would get if the whole population had been queried. In simple words, the margin of error is the product of critical value and the standard deviation.

The margin of error is denoted by E and the formula is given as,

$The\ margin\ of\ Error = z\times \frac{\sigma }{\sqrt{n}}$

where,

n= sample size

σ= Population Standard Deviation

z = z score

### Solved Examples

Question: A random sample of 30 students has average yearly earnings of 2450 and a standard deviation of 587. Find the margin of error if c = 0.95?

Solution:

Given
n=30, Standard Deviation= 587

σ = 587

c = 0.95

At 95% level of confidence z = 1.96

Margin of error = z × σ/√n

= 1.96 × 587/√30

= 1.96 × 107.12

= 209.96

= 210 (approx)