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Margin of Error Calculator
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Margin of error measurement indicates that the maximum deviation expected from the original population. It is a statistical measure. And it is not a calculator error but it is considered as the sampling error. Margin of error can be negative or positive. If the value of margin of error is less the calculated data is reliable or accurate. The formula to find out the margin of error is given as,

MOE=(1.96)$\sqrt{\frac{N-n}{N-1}}\times \sqrt{\frac{p(1-p)}{n}}$

Where N is the size of the population, n is the size of the sample and p is the probability of occurrence
Margin of error normally appeared as in percentage.

Steps for Margin of Error Calculator

Step 1 :

Find out the values of N, n, p from the question.

Step 2 :

Substitute values of these parameters in the given equation.

MOE=(1.96)$\sqrt{\frac{N-n}{N-1}}\times \sqrt{\frac{p(1-p)}{n}}$

Step 3 :

Convert the obtained value in percentage by multiplying it with 100.

Problems on Margin of Error Calculator

1. Calculate the margin of error, when a box contain 100 mangoes out of that 25 are not good. The probability of proportion is given as 0.2.

Step 1 :

The given parameters are
N= 100, n= 25, p= 0.2

Step 2 :

The equation is given by
MOE=(1.96)$\sqrt{\frac{N-n}{N-1}}\times \sqrt{\frac{p(1-p)}{n}}$
Substitute the values,
MOE=(1.96)$\sqrt{\frac{100-25}{100-1}}\times \sqrt{\frac{0.2(1-0.2)}{25}}$
MOE=1.96$\times \sqrt{0.7575}\times \sqrt{0.0064}$
MOE=1.96×0.8703×0.08=0.1364

Step 3 :

MOE=0.1364×100=13.64%

13.64%

2. A school bus contain total 50 students out of that 30 are boys. The probability of proportion is given by 0.1. Determine the margin of error?

Step 1 :

It is given that,
N=50, n=30, p=0.1

Step 2 :

MOE=(1.96)$\sqrt{\frac{N-n}{N-1}}\times \sqrt{\frac{p(1-p)}{n}}$
MOE=1.96$\times \sqrt{\frac{50-30}{50-1}}\times \sqrt{\frac{0.1(1-0.1)}{30}}$
MOE=1.96$\times \sqrt{0.4081}\times \sqrt{0.003}$
MOE=1.96×0.6388×0.0547=0.0684

Step 3 :

MOE=0.0684×100=6.84%