by Mean Deviation
Mean deviation is a measure of dispersion that indicates the average of the absolute differences between each data point and the mean (or median) of the dataset. It provides an overall sense of how much the values deviate from the central value. To calculate mean deviation, the absolute differences between each data point and the central measure are summed and then divided by the number of observations. Unlike variance, mean deviation is expressed in the same units as the data and is less sensitive to extreme outliers.
The basic formula for finding out mean deviation is :
Mean Deviation = Sum of absolute values of deviations from ‘a’ ÷ The number of observations
Standard Deviation
Standard deviation is a widely used measure of dispersion that indicates the average amount by which each data point deviates from the mean. It is calculated by first finding the variance, which is the average of squared deviations, and then taking the square root of the variance. Standard deviation provides a more interpretable measure of spread, as it is in the same units as the original data. A higher standard deviation indicates greater variability, while a lower value indicates data points are closer to the mean, indicating less spread or consistency.
Usually represented by s or σ. It uses the arithmetic mean of the distribution as the reference point and normalizes the deviation of all the data values from this mean.
Therefore, we define the formula for the standard deviation of the distribution of a variable X with n data points as:
