JEE Mains · Maths · STD 11 - 13. statistics
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
- A \(\phi\)
- B \(\{99\}\)
- C \(N\)
- D \(\{9\}\)
Answer & Solution
Correct Answer
(C) \(N\)
Step-by-step Solution
Detailed explanation
let \(a_1\) be any natural number \(a_1, a_1+1, a_1+2, \ldots ., a_1+99 \text { are values of } a_i ' S\) \(\bar{x}=\frac{a_1+\left(a_1+1\right)+\left(a_1+2\right)+\ldots . .+a_1+99}{100}\) \(=\frac{100 a_1+(1+2+\ldots . .+99)}{100}=a_1+\frac{99 \times 100}{2 \times 100}\)…
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