MHT CET · Maths · Probability
For the following frequency distribution
The variance is
- A 2.85
- B 2.18
- C 2.37
- D 2.49
Answer & Solution
Correct Answer
(A) 2.85
Step-by-step Solution
Detailed explanation
\(\begin{array}{cccc}\boldsymbol{x}_{\mathbf{i}} & \boldsymbol{f}_{\mathbf{i}} & \boldsymbol{f}_{\mathrm{i}} \boldsymbol{x}_{\mathbf{i}} & \boldsymbol{f}_{\mathbf{i}} \mathbf{x}_{\mathbf{i}}{ }^2 \\ 5 & 3 & 15 & 75 \\ 6 & 7 & 42 & 252 \\ 7 & 4 & 28 & 196 \\ 8 & 2 & 16 & 128 \\ 10 & \frac{4}{N=20} & \frac{40}{\sum f_i x_i=141} & \frac{400}{\sum f_i x_i^2=1051}\end{array}\)
\(\begin{aligned} & \text { Variance }=\frac{\sum f_i x_i^2}{N}-\left(\frac{\sum f_i x_i}{N}\right)^2 \\ & =\frac{1051}{20}-\left(\frac{141}{20}\right)^2 \\ & =52.55-(7.05)^2 \\ & =52.55-49.7025 \\ & =2.85\end{aligned}\)
\(\begin{aligned} & \text { Variance }=\frac{\sum f_i x_i^2}{N}-\left(\frac{\sum f_i x_i}{N}\right)^2 \\ & =\frac{1051}{20}-\left(\frac{141}{20}\right)^2 \\ & =52.55-(7.05)^2 \\ & =52.55-49.7025 \\ & =2.85\end{aligned}\)
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