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The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

JEE · Math · previous-year question

  1. A.2.4
  2. B.2.8correct
  3. C.2.5
  4. D.2.6

Answer

B. 2.8

Explanation

Let 5 observations are x1, x2, x3, x4, x5 given, x1 = 1, x2 = 2, x3 = 6 Mean = 5 $$ \therefore $$ Mean$$\left( {\overline x } \right)$$ = $${{{x_1} + {x_2} + {x_3} + {x_4} + {x_5}} \over 5}$$ = 5 $$ \Rightarrow $$ 1 + 2 + 6 + x4 + x5 = 25 $$ \therefore $$ x4 + x5 = 16 $$ \Rightarrow $$ (x4 $$-$$ 5) + (x5 $$-$$ 5) + 10 = 16 $$ \Rightarrow $$ (x4 $$-$$ 5) + (x5 $$-$$ 5) = 6 $$ \therefore $$ Mean deviation about mean, = $${{\sum {\left| {{x_i} - \overline x } \right|} } \over n}$$ = $${{\left| {1 - 5} \right| + \left| {2 - 5} \right| + \left| {6 - 5} \right| + \left| {{x_4} - 5} \right| + \left| {{x_5} - 5} \right|} \over 5}$$ = $${{4 + 3 + 1 + 6} \over 5}$$ = $${{14} \over 5}$$ = 2.8

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