# The ratio of standard deviation and square root of number of observations is called

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The ratio of standard deviation and square root of number of observations is called
1. RMS value
2. Variance
3. Optimum value
4. Standard error

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Correct Answer - Option 4 : Standard error

Concept:

The standard error (SE) of a statistic is the approximate standard deviation of a statistical sample population.

The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.

In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error of the mean.

Standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results.

For a sample size 'n' and $\bar {x}$;

The standard deviation (SD) is given by

$σ = \sqrt \frac { {\sum^n_{i=1} (x_i - \bar x)^2}}{n-1}$

Variance = σ2;

Now the standard error is given by

$\sigma _ {\bar {x}} = \frac {\sigma}{\sqrt {n}}$

From the above formula, it is clear that the Standard error of the sample mean is the ratio of standard deviation and the square root of the number of observations is called