Measures of Dispersion
2026-02-28 12:49 Diff
https://brightchamps.com/en-us/math/data/measures-of-dispersion

The absolute measure of dispersion is quantified and expressed in the same units as the data. Meters, kilograms, and dollars are some examples of the absolute measures of dispersion that are represented in the same units as the data. For instance, if the standard deviation of BVT company’s salary distribution is $700, it indicates that the salaries vary by around $700 from the mean. Here are some of the absolute measures of dispersion. 

Range: It is an absolute measure of dispersion that can be defined as the difference between the distribution’s maximum and minimum values. To calculate the range, the formula we can employ is:

\(\text{Range = H − S}\)


Here, H is the highest value and S is the smallest value in the dataset.

Mean deviation: It is the difference between each data point and the mean, calculated as arithmetic mean. The formula for finding the mean deviation is:


\(\text{Mean deviation} = \frac{\sum _{i=1}^n (x_i-\bar x)} {n}\)


Here, x̄ denotes the mean, median, or mode of the dataset and it is the central value.


n is the number of values and x​​​​i is the individual data point. 

Standard deviation: It is the square root of the mean of the squared deviations from the average value of the dataset. The formula for standard deviation is different for population standard deviation and sample standard deviation. Therefore, the formula of standard deviation is given as,

For population standard deviation:
 

\(\sigma = \sqrt{\sigma^{2}} \)

For sample standard deviation: 
 

\(s = \sqrt{s^{2}}\)

Variance: It is the mean or average of the squared deviations from the mean of the provided dataset. The formula for population variance is: 


 \(σ ^2 = {\sum _i ^n (x_i - \mu)^2 \over N}\)


The formula for calculating sample variance is:


\(S^2 = {{\sum_ i ^n (x_i - \bar x)^2 }\over n-1}\)


Here, xi refers to each value of a dataset.


x̄ is the mean. 

n is the number of values in the dataset. 

Interquartile range: It is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1). The formula used is \(Q_3 − Q_1\). Here, Q3 is the upper or the third quartile and Q1 is the lower or first quartile.