State whether the following statement is True or False and also give the reason in support of your answer.
b) Mean deviation is least when calculated from the median.
Solution
True.
Mean deviation is least when calculated from the median.
The median is a measure of central tendency that divides the data into two equal halves, with half of the observations above the median and half below. The mean deviation from the median is calculated as the sum of the absolute deviations from the median divided by the number of observations.
Since the median separates the data into two equal halves, the sum of deviations from the median is zero, meaning that the mean deviation from the median is the smallest possible value for any measure of central tendency. This makes the median a robust statistic, meaning it is less sensitive to outliers in the data compared to other measures of central tendency like the mean.
Hence given statement is true.