JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of \(7\) observations are \(8\) and \(16,\) respectively. If five observations are \(2, 4, 10,12,14,\) then the absolute difference of the remaining two observations is
- A \(2\)
- B \(4\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(\bar{x}=\frac{2+4+10+12+14+x+y}{7}=8\) \(x+y=14\) \((\sigma)^{2}=\frac{\sum\left( x _{ i }\right)^{2}}{ n }-\left(\frac{\sum x _{ i }}{ n }\right)^{2}\) \(16=\frac{4+16+100+144+196+x^{2}+y^{2}}{7}-8^{2}\) \(16+64=\frac{460+x^{2}+y^{2}}{7}\) \(560=460+x^{2}+y^{2}\)…
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 the position vectors of the points \(A , B , C\) and \(D\) be \(5 \hat{i}+5 \hat{j}+2 \lambda \hat{k}, \hat{i}+2 \hat{j}+3 \hat{k},-2 \hat{i}+\lambda \hat{j}+4 \hat{k}\) and \(-\hat{ i }+5 \hat{ j }+6 \hat{ k }\). Let the set \(S =\{\lambda \in R\) : The points \(A\), \(B , C\) and D are coplanar \(\}\). Then \(\sum_{\lambda \in S}(\lambda+2)^2\) is equal toJEE Mains 2023 Hard
- If \(A\) denotes the sum of all the coefficients in the expansion of \(\left(1-3 x+10 x^2\right)^n\) and \(B\) denotes the sum of all the coefficients in the expansion of \(\left(1+x^2\right)^n\), then :JEE Mains 2024 Medium
- A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point \(A\) on the path, he observes that the angle of elevation of the top of the pillar is \(30^o .\) After walking for \(10\) minutes from \(A\) in the same direction, at a point \(B,\) he observes that the angle of elevation of the top of the pillar is \(60^o .\) Then the time taken (in minutes) by him, from \(B\) to reach the pillar, is:JEE Mains 2016 Hard
- The number of ways, in which \(5\) girls and \(7\) boys can be seated at a round table so that no two girls sit together, isJEE Mains 2023 Medium
- The area bounded by the curve \(4 y^{2}=x^{2}(4-x)(x-2)\) is equal to ...... .JEE Mains 2021 Hard
- \(\lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2} \sin 2 x}\) is equal toJEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(f(x)=3 \sqrt{x-2}+\sqrt{4-x}\) be a real valued function. If \(\alpha\) and \(\beta\) are respectively the minimum and the maximum values of \(\mathrm{f}\), then \(\alpha^2+2 \beta^2\) is equal toJEE Mains 2024 Hard
- Let \(R\) be a relation defined on \(N\) as a \(R\) b is \(2 a+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) isJEE Mains 2023 Medium
- Let two vertices of triangle \(ABC\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=11\) is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal toJEE Mains 2023 Hard
- A function \(f\) is defined on \([-3,3]\) as \(f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}\right\} & , \quad-2 \leq x \leq 2 \\ {[|x|]} & , \quad 2<|x| \leq 3\end{array}\right.\) where \([x]\) denotes the greatest integer \(\leq x .\) The number of points, where \(f\) is not differentiable in \((-3,3)\) isJEE Mains 2021 Hard
- On the ellipse \(\frac{x^{2}}{8}+\frac{y^{2}}{4}=1\) let \(P\) be a point in the second quadrant such that the tangent at \(\mathrm{P}\) to the ellipse is perpendicular to the line \(x+2 y=0\). Let \(S\) and \(\mathrm{S}^{\prime}\) be the foci of the ellipse and \(\mathrm{e}\) be its eccentricity. If \(\mathrm{A}\) is the area of the triangle \(SPS'\) then, the value of \(\left(5-\mathrm{e}^{2}\right) . \mathrm{A}\) is :JEE Mains 2021 Hard
- If \(2 x^y+3 y^x=20\), then \(\frac{d y}{d x}\) at \((2,2)\) is equal toJEE Mains 2023 Hard