Consider the data of scores obtained by students in an examination. If the score of every student is increased by 2 marks, then which of the following statements is TRUE?

Step-by-step solution

Let the original scores be x₁, x₂, , x_n . When every score is increased by 2 , the new scores are y_i = x_i + 2 . The new mean is y = x + 2 . The mean deviation about the mean for the new scores is 1 n |y_i - y | . Substituting the values, we get 1 n |(x_i + 2) - ( x + 2)| = 1 n |x_i - x | . This is exactly equal to the original mean deviation about the mean. Thus, the mean deviation about the mean does not change. Similarly, all measures of dispersion like variance, standard deviation, and mean deviation about th