MHT CET · Maths · Statistics
The variance of 20 observations is 5. If each observation is multiplied by 3 and then 8 is added to each number, then variance of resulting observations is
- A 35
- B 55
- C 25
- D 45
Answer & Solution
Correct Answer
(D) 45
Step-by-step Solution
Detailed explanation
- Variance Calculation:
- Given: Variance \(=5\) for 20 observations.
- Each observation is multiplied by 3: Variance gets multiplied by \(3^2=\)
- New variance:
\(\text {New variance }=9 \times 5=45\)
- Adding 8 to each observation does not change the variance.
- Final variance: 45.
Answer: 45, which matches the solution shown.
- Given: Variance \(=5\) for 20 observations.
- Each observation is multiplied by 3: Variance gets multiplied by \(3^2=\)
- New variance:
\(\text {New variance }=9 \times 5=45\)
- Adding 8 to each observation does not change the variance.
- Final variance: 45.
Answer: 45, which matches the solution shown.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The value of the integral \(\int_1^2 \frac{x \mathrm{~d} x}{(x+2)(x+3)}\) isMHT CET 2025 Medium
- The area of the region bounded by the curve \(y^2=4 x\) and the line \(y=x\) isMHT CET 2021 Easy
- The joint equation of pair of lines through the origin and making equilateral triangle with the line \(y=4\) isMHT CET 2020 Easy
- If the function \(f\) defined by \(f(x)=K\left(x-x^{2}\right)\) if \(0 < x < 1\)
\(=0 \quad, \quad\) other wise
is the p.d.f. of a r. v. \(X\), then the value of \(P\left(X < \frac{1}{2}\right)\) isMHT CET 2020 Medium - If \(\mathrm{A}+\mathrm{B}=\frac{\pi}{2}\) then the maximum value of \(\cos \mathrm{A} \cdot \cos \mathrm{B}\) isMHT CET 2025 Medium
- If \(\mathrm{f}(x)=\frac{\sin ^2 x}{1+\cot x}+\frac{\cos ^2 x}{1+\tan x}\), then the value of \(\mathrm{f}^{\prime}\left(\frac{\pi}{6}\right)\) is equal toMHT CET 2025 Medium
More PYQs from MHT CET
- If \(\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha\), then \(\alpha=\)MHT CET 2021 Medium
- Which from following is a mineral of copper?MHT CET 2024 Medium
- The distance of the plane \(\overline{\mathrm{r}}=(\hat{i}-\hat{\mathrm{j}})+\lambda(\hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(\hat{i}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})\) from the origin isMHT CET 2025 Medium
- Self-pollination which involves two different flowers of the same plant, is calledMHT CET 2015 Easy
- Which cation from following exhibits no magnetic moment?MHT CET 2025 Medium
- The translational kinetic energy of the molecules of a gas at absolute temperature \(T\) can be doubled byMHT CET 2022 Easy