1. Tardigrade
  2. Question
  3. Mathematics
  4. If a variable takes discrete values x + 4, x - (7/2) ,x - (5/2) , x - 3, x - 2, x + (1/2) , x - (1/2), x + 5 (x is positive), then the median is :

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Q. If a variable takes discrete values $ x + 4, x - \frac{7}{2} ,x - \frac{5}{2} , x - 3, x - 2, x + \frac{1}{2} , x - \frac{1}{2}, x + 5$ (x is positive), then the median is :

Statistics

Solution:

First we arrange the given data in ascending or descending order we have
$ x + 5, x + 4 , x + \frac{1}{2} ,x - \frac{1}{2} , x - 2, x - \frac{5}{2} , x - 3,x - \frac{7}{2} $
Total no. of observation = 8 (even)
$\therefore \:\: $ Median $= \frac{4^{th}\, \text{observation} + 5^{th}\, \text{observation}}{2}$
$ = \frac{x - 1 /2 +x - 2}{2} = \frac{ 2x - \frac{1}{2} - 2}{2} = x - 5 / 4$