The mean deviation from the median is:
options: A. Equal to that measured from another value B. Maximum if all the observations are positive C. Greater than that measured from any other value D. Less than that measured from any value
The correct answer and explanation is:
The correct answer is C. Greater than that measured from any other value.
Explanation:
The mean deviation from the median refers to the average of the absolute differences between each data point and the median of the data set. The median is the middle value when the data is arranged in ascending or descending order.
One key property of the median is that it minimizes the sum of absolute deviations compared to other measures of central tendency, such as the mean. In other words, the sum of the absolute differences from the median is smaller than the sum of absolute differences from any other central point (like the mean or mode).
When the data points are spread out and symmetric around the median, the mean deviation from the median is smaller than the mean deviation from other values. This characteristic makes the median a more robust measure of central tendency, particularly in the presence of outliers or skewed distributions.
For example, if you have a data set with outliers, the median remains less influenced by those extreme values compared to the mean. The mean deviation from the median will be relatively smaller than that from the mean, which can be pulled towards the outliers. In symmetric distributions, the median balances the data well, making the mean deviation from it the least compared to any other value.
In conclusion, the mean deviation from the median is the smallest and cannot be greater than the deviation from the median for any other value. Therefore, the correct answer is C.