JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of \(20\) observations are found to be \(10\) and \(4,\) respectively. On rechecking, it was found that an observation \(9\) was incorrect and the correct observation was \(11\). Then the correct variance is
- A \(3.99\)
- B \(3.98\)
- C \(4.02\)
- D \(4.01\)
Answer & Solution
Correct Answer
(A) \(3.99\)
Step-by-step Solution
Detailed explanation
\(\frac{\sum \mathrm{x}_{\mathrm{i}}}{20}=10 \Rightarrow \Sigma \mathrm{x}_{\mathrm{i}}=200\) \(\frac{\sum \mathrm{x}_{\mathrm{i}}^{2}}{20}-100=4 \Rightarrow \Sigma \mathrm{x}_{\mathrm{i}}^{2}=2080\) Actual mean \(=\frac{200-9+11}{20}=\frac{202}{20}\) Variance…
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
- Let \(\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}\). If \(\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathrm{N}\), then \(3(\mathrm{~b}+\mathrm{c})\) is equal toJEE Mains 2025 Hard
- If \(\frac{d x}{d y}=\frac{1+x-y^2}{y}, x(1)=1\), then \(5 x(2)\) is equal to :JEE Mains 2024 Hard
- The set of all real values of \(\lambda\) for which the quadratic equations, \(\left(\lambda^{2}+1\right) x ^{2}-4 \lambda x +2=0\) always have exactly one root in the interval \((0,1)\) isJEE Mains 2020 Hard
- Consider two circles \(C_1: x^2+y^2=25\) and \(C_2:(x-\) \(\alpha)^2+y^2=16\), where \(\alpha \in(5,9)\). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) be \(\sin ^{-1}\left(\frac{\sqrt{63}}{8}\right)\). If the length of common chord of \(C_1\) and \(C_2\) is \(\beta\), then the value of \((\alpha \beta)^2\) equalsJEE Mains 2024 Hard
- Let a vertical tower \(AB\) of height \(2 h\) stands on a horizontal ground. Let from a point \(P\) on the ground a man can see upto height \(h\) of the tower with an angle of elevation \(2 \alpha\). When from \(P\), he moves a distance \(d\) in the direction of \(\overline{A P}\), he can see the top B of the tower with an angle of elevation \(\alpha\). If \(d=\sqrt{7} h\), then \(\tan \alpha\) is equal to.JEE Mains 2022 Hard
- The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\), isJEE Mains 2023 Medium
More PYQs from JEE Mains
- Let \(A=\{(\alpha, \beta) \in \mathbf{R} \times \mathbf{R}:|\alpha-1| \leq 4 \text { and }|\beta-5| \leq 6\}\) and \(B=\{(\alpha, \beta) \in \mathbf{R} \times\) \(\mathbf{R}: 16(\alpha-2)^2+9(\beta-6)^2 \leq 144\}\)JEE Mains 2025 Easy
- Let \(f:[-1,2] \rightarrow \mathrm{R}\) be given by \(f(x)=2 x^2+x+\left[x^2\right]-[x]\), where \([t]\) denotes the greatest integer less than or equal to \(t\). The number of points, where \(f\) is not continuous, is :JEE Mains 2024 Hard
- Let \(\hat{a}, \hat{b}\) be unit vectors. If \(\vec{c}\) be a vector such that the angle between \(\hat{ a }\) and \(\overrightarrow{ c }\) is \(\frac{\pi}{12}\), and \(\hat{ b }=\overrightarrow{ c }+2(\overrightarrow{ c } \times \hat{ a })\), then \(|6 \overrightarrow{ c }|^{2}\) is equal toJEE Mains 2022 Hard
- If \(A=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], C=\mathrm{ABA}^{\mathrm{T}}\) and \(\mathrm{X}\) \(=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}\), then \(\operatorname{det} \mathrm{X}\) is equal to :JEE Mains 2024 Hard
- Let one end of a focal chord of the parabola \( y^{2}=16x \) be (16, 16). If \( P(\alpha,\beta) \) divides this focal chord internally in the ratio 5 : 2 then the minimum value of \( \alpha+\beta \) is equal to :JEE Mains 2026 Medium
- If \(\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11\), then \(n\) satisfies the equationJEE Mains 2016 Hard