The square root of the variance is:

Correct option is C

The standard deviation (σ) is defined as the square root of the variance (σ²). It measures the dispersion or spread of a dataset relative to its mean. The standard deviation provides a clearer interpretation of variability because it is expressed in the same units as the data, unlike variance, which is in squared units.

Mathematically,

​σ =$$\sqrt{\frac{\sum (X - \bar{X})^2}{N}}$$

where:

​$\sigma$ = Standard deviation

$$\bar{X}$$​ Mean of the dataset

$X$ = Individual data points

$N$ = Number of observations​

• Variance measures how far each number in a dataset is from the mean, but its unit is squared.
• Standard deviation makes the measurement more interpretable by taking the square root of the variance.
• Used in: Economics, social sciences, geography, and statistical research for analyzing variability in data.

1. (a) Mean deviation – Incorrect

   • Mean deviation is the average of absolute differences from the mean, not the square root of variance.

2. (b) Coefficient of mean deviation – Incorrect

   • The coefficient of mean deviation is a relative measure, calculated as Mean Deviation / Mean, not related to variance.

3. (d) Coefficient of standard deviation – Incorrect

   • It is a measure of relative dispersion, calculated as Standard Deviation / Mean, and not the square root of variance.

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