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Question: If a variable takes the discrete values \(\alpha - 4,\alpha - \frac{7}{2},\alpha - \frac{5}{2},\alp...

If a variable takes the discrete values

α−4,α−72,α−52,α−3,α−2,α+12,α−12,α+5(α>0)\alpha - 4,\alpha - \frac{7}{2},\alpha - \frac{5}{2},\alpha - 3,\alpha - 2,\alpha + \frac{1}{2},\alpha - \frac{1}{2},\alpha + 5(\alpha > 0), then the median is

A

α−54\alpha - \frac{5}{4}

B

α−12\alpha - \frac{1}{2}

C

α−2\alpha - 2

D

α+54\alpha + \frac{5}{4}

Answer

α−54\alpha - \frac{5}{4}

Explanation

Solution

Arrange the data as

α−72,α−3,α−52,α−2,α−12,α+12,α+4,α+5\alpha - \frac{7}{2},\alpha - 3,\alpha - \frac{5}{2},\alpha - 2,\alpha - \frac{1}{2},\alpha + \frac{1}{2},\alpha + 4,\alpha + 5

Median=12[value of 4thitem+value of 5thitem]= \frac{1}{2}\lbrack\text{value of }\text{4}^{\text{th}}\text{item} + \text{value of }\text{5}^{\text{th}}\text{item}\rbrack

∴ Median =α−2+α−122= \frac{\alpha - 2 + \alpha - \frac{1}{2}}{2} =2α−522= \frac{2\alpha - \frac{5}{2}}{2}= α−54\alpha - \frac{5}{4}.