# What is the difference between the standard deviation and margin of error?

##### 1 Answer

Both characterize the quality of approximation of some unknown constant with results of its statistical evaluation.

Knowing one of them, we can determine another.

#### Explanation:

*Theory*:

When values of the random variable *mathematical expectation* *standard deviation* *confidence interval* of a radius

"With probability

Given any required probability

Obviously, the higher required probability with a given standard deviation

On the other hand, if probability

Radius of the confidence interval *margin of error*.

*Example*:

100 people measure the length of a car.

Their results

Let's approximate unknown

and approximate unknown

Knowing these approximate values and fundamental properties of the normal distribution, for a given probability *margin of error*

So, we can say that with probability

As you see, standard deviation and margin of error are functionally dependent.