MHT CET · Maths · Statistics
In an experiment with 15 observations for \(x\), the following results were available \(\sum x^2=2830, \sum x=170\). One observation 20 was found to be wrong and was replaced by the correct value 30 . Then the corrected variance is
- A 78
- B 210
- C 225
- D 88
Answer & Solution
Correct Answer
(A) 78
Step-by-step Solution
Detailed explanation
Given: \(\sum x=170\) and \(\sum x^2=2830\)
Corrected sum
\(\begin{aligned}
& \sum x=170-20+30=180 \\
& \sum x^2=2830-400+900=3330
\end{aligned}\)
\(\therefore \quad\) Corrected variance
\(\begin{aligned}
& =\left(\frac{\sum x^2}{n}\right)-\left(\frac{\sum x}{n}\right)^2 \\
& =\left(\frac{3330}{15}\right)-\left(\frac{180}{15}\right)^2 \\
& =222-144=78
\end{aligned}\)
Corrected sum
\(\begin{aligned}
& \sum x=170-20+30=180 \\
& \sum x^2=2830-400+900=3330
\end{aligned}\)
\(\therefore \quad\) Corrected variance
\(\begin{aligned}
& =\left(\frac{\sum x^2}{n}\right)-\left(\frac{\sum x}{n}\right)^2 \\
& =\left(\frac{3330}{15}\right)-\left(\frac{180}{15}\right)^2 \\
& =222-144=78
\end{aligned}\)
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
- General solution of the differential equation \(\sin ^3 \mathrm{x} \frac{\mathrm{dx}}{\mathrm{dy}}=\sin \mathrm{y}\) is given byMHT CET 2022 Easy
- If \(\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -2 & -2 \\ 1 & 3 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}0 \\ 3 \\ 4\end{array}\right]\), then \(2 x-y+z=\)MHT CET 2022 Easy
- \(\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] \mathrm{d} x, x>0=\)MHT CET 2023 Hard
- If the function \(\mathrm{f}(x)=x(x+3) \mathrm{e}^{-\frac{x}{2}}\) satisfies all the conditions of Rolle's theorem in \([-3,0]\), then c isMHT CET 2025 Easy
- \(\int \frac{\sec ^8 x}{\operatorname{cosec} x} d x=\)MHT CET 2021 Hard
- There are 6 periods in each working day of a school. The number of ways one can arrange 5 subjects such that each is allowed at least one period, isMHT CET 2022 Medium
More PYQs from MHT CET
- If a complex number \(\mathrm{z}=\frac{4+3 i \sin \theta}{1-2 i \sin \theta}(\) where \(i=\sqrt{-1})\) is purely real, then the value of \(\theta\) isMHT CET 2025 Medium
- Calculate \(\Delta \mathrm{H}\) for following reaction, at \(25^{\circ} \mathrm{C}\). Calculate \(\Delta \mathrm{H}\) for following reaction, at \(25^{\circ} \mathrm{C}\).
\(\mathrm{NH}_2 \mathrm{CN}_{(\mathrm{g})}+\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \longrightarrow \mathrm{N}_{2(\mathrm{~g})}+\mathrm{CO}_{2(\mathrm{~g})}+\) \(\mathrm{H}_2 \mathrm{O}_{(l)} \ (\Delta \mathrm{U}=-740.5 \mathrm{~kJ}, \mathrm{R}=\) \(8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1})\)MHT CET 2023 Medium - Calculate the \(\mathrm{pH}\) of \(0.01 \mathrm{M}\) strong dibasic acid.MHT CET 2023 Easy
- Which one of the following plant hormones is NOT a growth promoter?MHT CET 2025 Hard
- \(\sin 690^{\circ} \times \sec 240^{\circ}=\)MHT CET 2020 Easy
- Which from following elements is most abundant on earth?MHT CET 2023 Easy