JEE Mains · Maths · STD 11 - 13. statistics
The mean of five observations is \(5\) and their variance is \(9.20\). If three of the given five observations are \(1, 3\) and \(8\), then a ratio of other two observations is
- A \(10 : 3\)
- B \(4 : 9\)
- C \(5 : 8\)
- D \(6 : 7\)
Answer & Solution
Correct Answer
(B) \(4 : 9\)
Step-by-step Solution
Detailed explanation
\(\mu = \frac{{1 + 3 + 8 + x + y}}{5}\) \(25 = 12 + x + y \Rightarrow x + y = 13\,\,\,\,\,\,\,\,........\left( 1 \right)\) \({\sigma ^2} = \frac{{\sum {{{\left( {{x_i} - \mu } \right)}^2}} }}{N}\) \(9.2 = \frac{{1 + 9 + 64 + {x^2} + {y^2}}}{5} - 25\)…
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
- If \( (\frac{1}{^{15}C_{0}}+\frac{1}{^{15}C_{1}})(\frac{1}{^{15}C_{1}}+\frac{1}{^{15}C_{2}})...(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}) = \frac{a^{13}}{^{14}C_{0}^{14}C_{1}...^{14}C_{12}} \) then 30a is equal to :JEE Mains 2026 Medium
- For any three positive real numbers \(a,b,c\) ; \(9\left( {25{a^2} + {b^2}} \right) + 25\left( {{c^2} - 3ac} \right) = 15b\left( {3a + c} \right)\) thenJEE Mains 2017 Hard
- The number of permutations, of the digits \(1,2,3,...7\) without repetition, which neither contain the string \(153\) nor the string \(2467\), is \(........\).JEE Mains 2023 Hard
- Let \(\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}\) be a sample space and \(A=\{M \in S: M\) is invertible \(\}\) be an event. Then \(P ( A )\) is equal toJEE Mains 2023 Hard
- If \(A\) is a symmetric matrix and \(B\) is a skew-symmetrix matrix such that \(A + B = \left[ {\begin{array}{*{20}{c}}
2&3\\
5&{ - 1}
\end{array}} \right]\) , then \(AB\) is equal toJEE Mains 2019 Hard - If the length of the latus rectum of the ellipse \(x^{2}+\) \(4 y^{2}+2 x+8 y-\lambda=0\) is \(4\) , and \(l\) is the length of its major axis, then \(\lambda+l\) is equal to\(......\)JEE Mains 2022 Medium
More PYQs from JEE Mains
- The number of points of intersection of \(| z -(4+3 i )|=2\) and \(| z |+| z -4|=6, z \in C\) isJEE Mains 2022 Medium
- Let the area of the triangle formed by a straight Line L: \(\mathrm{x}+\mathrm{by}+\mathrm{c}=0\) with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of \(45^{\circ}\) with the positive x -axis, then the value of \(\mathrm{b}^2+\mathrm{c}^2\) is:JEE Mains 2025 Easy
- Consider the following system of equations : \(x+2 y-3 z=a\) ; \(2 x+6 y-11 z=b\) ; \(x-2 y+7 z=c\) where \(a , b\) and \(c\) are real constants. Then the system of equations :JEE Mains 2021 Medium
- The minimum value of \(\alpha\) for which the equation \(\frac{4}{\sin x}+\frac{1}{1-\sin x}=\alpha\) has at least one solution in \(\left(0, \frac{\pi}{2}\right)\) is ..........JEE Mains 2021 Medium
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{ dy }{ dx }+\left(\frac{2 x ^{2}+11 x +13}{ x ^{3}+6 x ^{2}+11 x +6}\right)\) \(y=\frac{(x+3)}{x+1}, x>-1\), which passes through the point \((0,1)\). Then \(y (1)\) is equal to.JEE Mains 2022 Hard
- The equation of the chord, of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), whose mid-point is \((3,1)\) is :JEE Mains 2025 Medium