Verified Solution • 2025–26 Session moderate

QJEEM24Ma9d47: JEE Main 2024 Mathematics - Class 11 JEEM24Ma9d47 Solution: If the variance of the frequency distribution .tg…

If the variance of the frequency distribution

xx cc 2c2c 3c3c 4c4c 5c5c 6c6c
ff 2 1 1 1 1 1

is 160, then the value of c∈Nc\in N is

Multiple Choice Options

  • A 5
  • B 8
  • C 6
  • D 7

Step-by-Step Verified Solution

xix_i f(xi)f(x_i) x(f(x)x(f(x) x2f(x)x^2f(x)
C 2 2C 2C 2^2
2C 1 2C 4C 2^2
3C 1 3C 9C 2^2
4C 1 4C 16C 2^2
5C 1 5C 25C 2^2
6C 1 6C 36C 2^2

amp;σ2=E(x2)−[E(x)],∑f(xi)=7amp;E(x)=∑xf(x)=22Camp;E(x2)=∑x2f(x)=92C2\begin{aligned}& \sigma^2=E\left(x^2\right)-[E(x)], \sum f\left(x_i\right)=7 \\& E(x)=\sum x f(x)=22 C \\& E\left(x^2\right)=\sum x^2 f(x)=92 C^2\end{aligned}

amp;σ2=160=92C27−(22C7)2amp;⇒C=±7 but C∈Namp;⇒C=7\begin{aligned}& \sigma^2=160=\frac{92 C^2}{7}-\left(\frac{22 C}{7}\right)^2 \\& \Rightarrow C= \pm 7 \text { but } C \in N \\& \Rightarrow C=7\end{aligned}

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