Multiple choice

Mean deviation for $n$ observations ${ x }{ 1 },{ x }{ 2 },.....{ x }_{ n }$ from their mean $\bar { X } $ is given by:

  1. $\sum _{ i=1 }^{ n }{ ( { x }_{ i }-\bar { X }) }$
  2. $\cfrac { 1 }{ n } \sum _{ i=1 }^{ n }{ \left| { x }_{ i }-\bar { X } \right| } $
  3. $\sum _{ i=1 }^{ n }{ { { (x }_{ i }-\bar { X } ) }^{ 2 } }$
  4. $\cfrac { 1 }{ n } \sum _{ i=1 }^{ n }{ { { (x }_{ i }-\bar { X } ) }^{ 2 } } $
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B Correct answer
Explanation

Mean deviation from the mean is defined as the average of the absolute differences between each observation and the mean. This is represented by (1/n) * sum(|xi - mean|).

AI explanation

The mean deviation from the mean measures the average distance of all observations from their central tendency. To compute it, you find the absolute value of the difference between each observation and the arithmetic mean to remove negative signs. The formula is 1 over n times the sum from i equals 1 to n of the absolute value of (x_i minus the mean).

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