Multiple choice

Let $\overline X$ and M.D. be the mean and the mean deviation about $\overline X$ of n observations $x_i, i=1, 2, ....., n.$ If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are :

  1. $\overline X, M.D.$
  2. $\overline X+5, M.D.$
  3. $\overline X, M.D. +5$
  4. $\overline X+5m, M.D.+5$
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B Correct answer
Explanation

Adding a constant to all observations shifts the mean by that constant but does not change the mean deviation, as the distances between observations remain the same.

AI explanation

Using the properties of central tendency and dispersion, when a constant value is added to every observation, the mean increases by that same constant. Since mean deviation about the mean is a measure of dispersion that depends on the differences between the observations and the mean, it remains completely unaffected by the addition of a constant to all data points. Therefore, if each observation is increased by 5, the new mean becomes X bar plus 5, while the new mean deviation remains M.D.

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