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JEE Main 20203 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
3 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2020 · 3 September · Morning Shift · Mathematics · Statistics

For the frequency distribution: Variate (x): x _ 1 , x _ 2 , x _ 3...

For the frequency distribution: Variate (x):x1,x2,x3,…,x15\left(x\right): {x}_{1}, {x}_{2}, {x}_{3}, \ldots , {x}_{15}
Frequency \left(f\right): {f}_{1}, {f}_{2}, {f}_{3}, \ldots , {f}_{15}<br/>where<br />where0 < {x}_{1} < {x}_{2} < {x}_{3} < \ldots < {x}_{15} = 10 and ∑i=115fi>0,\mathop{∑}_{i = 1}^{15}{f}_{i} > 0, the standard deviation cannot be

Options

  1. A44
  2. B11
  3. C66
  4. D22

Correct answer

C. 66

Step-by-step solution

We know σ2≤14(M−m)2{\sigma}^{2} \le \dfrac{1}{4}{\left(M - m\right)}^{2}.

Where MM is upper bound of value of any random variable and mm is lower bound of any random variable,

⇒σ2≤14(10−0)2⇒ {\sigma}^{2} \le \dfrac{1}{4}{\left(10 - 0\right)}^{2}

⇒σ2<25⇒ {\sigma}^{2} < 25, (removed equality sign because m>0m > 0)

⇒−5<σ<5⇒ - 5 < \sigma < 5

From given options σ≠6\sigma \ne 6.

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