# Difference Between Variance and Standard Deviation with Proper Definition and Brief Explanation

Dispersion indicates the extent to which observations deviate from an appropriate measure of central tendency. The measures of dispersion are divided into two categories, that is, an absolute measure of dispersion and a relative measure of dispersion. Variance and standard deviation are two types of an absolute measure of variability; which describes how the observations are spread around the mean. **Difference** It is not more than the mean of the squares of the deviations.,

other than, **standard deviation** is the square root of the numerical value obtained by calculating the variance. Many people contrast these two mathematical concepts. Therefore, this article attempts to clarify the important difference between variance and standard deviation.

## Content: Variation Vs Standard Deviation

- Comparative graph
- Definition
- Key differences
- Illustration
- Similarities
- conclusion

### Comparative graph

Basis for comparison | Difference | Standard deviation |
---|---|---|

Sense |
The variance is a numerical value that describes the variability of the observations from their arithmetic mean. | Standard deviation is a measure of the dispersion of observations within a data set. |

What is it? |
It is the average of the squared deviations. | It is the mean squared deviation. |

Tagged as |
Square sigma (σ ^ 2) | Sigma (σ) |

Expressed in |
Square units | The same units as the values in the data set. |

Indicates |
How far apart are individuals in a group? | How many observations in a data set differ from its mean? |

### Definition of variance

In statistics, variance is defined as the measure of variability that represents the extent of the members of a group. Find the average degree to which each observation varies from the mean. When the variance of a data set is small, it shows how close the data points are to the mean, while a higher variance value represents that the observations are widely dispersed around the arithmetic mean and with each other.

**For unclassified data** :

**For the grouped frequency distribution** :

### Definition of standard deviation

Standard deviation is a measure that quantifies the amount of dispersion of the observations in a data set. The low standard deviation is an indicator of the closeness of the scores to the arithmetic mean and represents a high standard deviation; Scores are spread out over a higher range of values.

**For unclassified data** :

**For pooled frequency distribution** :

## Key differences between variance and standard deviation

The difference between the standard deviation and the variance can be clearly established for the following reasons:

- The variance is a numerical value that describes the variability of the observations from their arithmetic mean. Standard deviation is a measure of the dispersion of observations within a data set.
- The variance is nothing more than an average of the squared deviations. On the other hand, the standard deviation is the mean squared deviation.
- The variance is denoted by sigma-squared (σ
^{2}) while the standard deviation is labeled as sigma (σ). - Variation is expressed in square units that are generally larger than the values in the given data set. As opposed to the standard deviation which is expressed in the same units as the values in the data set.
- Variance measures how far apart individuals are in a group. Conversely, the standard deviation measures the number of observations in a data set that differs from its mean.

### Illustration

The grades obtained by a student in five subjects are 60, 75, 46, 58 and 80 respectively. You have to find the standard deviation and the variance.

First, you have to find the mean.,

So the mean (mean) marks are 63.8

Now calculate the variance

X | A | (x-A) | (X-A) ^ 2 |
---|---|---|---|

60 | 63.8 | -3.8 | 14.44 |

75 | 63.8 | 11.2 | 125.44 |

46 | 63.8 | -17.8 | 316.84 |

58 | 63.8 | 5.8 | 33.64 |

80 | 63.8 | 16.2 | 262.44 |

Where, X = Observations

A = arithmetic mean

So the variance is 150.56.

And the standard deviation is –

### Similarities

- Both the variance and the standard deviation are always positive.
- If all the observations in a data set are identical, then the standard deviation and the variance will be zero.

### conclusion

These two are basic statistical terms, which play a vital role in different sectors. Standard deviation is preferred over the mean, as it is expressed in the same units as the measurements, while the variance is expressed in units larger than the given data set.