QJEEM23Ma6f77: JEE Main 2023 Mathematics - Class 11 JEEM23Ma6f77 Solution: Let be the set of all values of for which the mean deviation…

Question

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Let

S

be the set of all values of

a_1

for which the mean deviation about the mean of 100 consecutive positive integers

a_1, a_2, a_3, \ldots ., a_{100}

is 25 . Then

S

is :

Accepted Answer

Let $a_{1} = a \Rightarrow a_{2} = a + 1, . . . . . a_{100} = a + 90$

$μ = \frac{\frac{100 a + (99 \times 100)}{2}}{100} = a + \frac{99}{2}$

M.D $= \frac{\sum | a_{1} - μ |}{100} = \frac{{(\frac{99}{2} + \frac{97}{2} + . . . + \frac{1}{2})}^{2}}{100} = \frac{2500}{100} = 25$

$∴$ $a \to z$

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