JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of \(7\) observations are \(8\) and \(16\) respectively. If one observation \(14\) is omitted a and \(b\) are respectively mean and variance of remaining \(6\) observation, then \(a+3 b-5\) is equal to \(..........\).
- A \(36\)
- B \(35\)
- C \(34\)
- D \(37\)
Answer & Solution
Correct Answer
(D) \(37\)
Step-by-step Solution
Detailed explanation
\(\frac{x_1+x_2+\ldots .+x_7}{7}=8\) \(\frac{x_1+x_2+x_3 \ldots .+x_6+14}{7}=8\) \(\Rightarrow x_1+x_2+\ldots .+x_6=42\) \(\therefore \frac{x_1+x_2 \ldots .+x_6}{6}=\frac{42}{6}=7=a\) \(\frac{\sum x_i^2}{7}-8^2=16\) \(\Rightarrow x^2=560\)…
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 surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is \(3\) units and after \(5\) seconds, it becomes \(7\) units, then its radius after \(9\) seconds isJEE Mains 2022 Medium
- Let \(a _1, a _2, a _3, \ldots\) be a \(G.P.\) of increasing positive numbers. Let the sum of its \(6^{\text {th }}\) and \(8^{\text {th }}\) terms be \(2\) and the product of its \(3^{\text {rd }}\) and \(5^{\text {th }}\) terms be \(\frac{1}{9}\). Then \(6\left( a _2+\right.\) \(\left.a_4\right)\left(a_4+a_6\right)\) is equal toJEE Mains 2023 Hard
- Let \(y=y(t)\) be a solution of the differential equation \(\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}\) Where, \(\alpha > 0, \beta > 0\) and \(\gamma > 0\). Then \(\operatorname{Lim}_{t \rightarrow \infty} y(t)\)JEE Mains 2023 Hard
- In a box, there are \(20\) cards, out of which \(10\) are lebelled as \(\mathrm{A}\) and the remaining \(10\) are labelled as \(B\). Cards are drawn at random, one after the other and with replacement, till a second \(A-\)card is obtained. The probability that the second \(A-\)card appears before the third \(B-\)card isJEE Mains 2020 Hard
- Twenty metres of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is :JEE Mains 2017 Hard
- The imaginary part of \((3+2 \sqrt{-54})^{1 / 2}-(3-2 \sqrt{-54})^{1 / 2}\) can beJEE Mains 2020 Medium
More PYQs from JEE Mains
- If \(z=x+i y, x y \neq 0\), satisfies the equation \(z^2+i \bar{z}=0\), then \(\left|z^2\right|\) is equal to :JEE Mains 2024 Medium
- Let \(9\) distinct balls be distributed among \(4\) boxes, \(B_{1}, B_{2}, B_{3}\) and \(B_{4}\). If the probability that \(B_{3}\) contains exactly \(3\) balls is \(k\left(\frac{3}{4}\right)^{9}\) then \(\mathrm{k}\) lies in the set:JEE Mains 2021 Hard
- Let the position vectors of two points \(P\) and \(Q\) be \(3 \hat{ i }-\hat{ j }+2 \hat{ k }\) and \(\hat{ i }+2 \hat{ j }-4 \hat{ k },\) respectively. Let \(R\) and \(S\) be two points such that the direction ratios of lines \(PR\) and \(QS\) are \((4,-1,2)\) and \((-2,1,-2),\) respectively. Let lines \(PR\) and \(QS\) intersect at \(T\). If the vector \(\overline{ TA }\) is perpendicular to both \(\overline{ PR }\) and \(\overline{ QS }\) and the length of vector \(\overline{ TA }\) is \(\sqrt{5}\) units, then the modulus of a position vector of \(A\) isJEE Mains 2021 Hard
- If the system of linear equations \(x_1 + 2x_2 + 3x_3 = 6\) ; \(x_1 + 3x_2 + 5x_3 = 9\) ; \(2x_1 + 5x_2 + ax_3 = b\) is consistent and has infinite number of solutions, thenJEE Mains 2013 Hard
- Let \(f(x) = - 1 + \left| {x - 2} \right|,\) and \(g(x) = 1 - \left| x \right|;\) then the set of all points where \(fog\) is discontinuous isJEE Mains 2013 Hard
- Let \(e_1\) and \(e_2\) be two distinct roots of the equation \(x^2 - ax + 2 = 0\). Let the sets \(\{a \in \mathbb{R} : e_1 \text{ and } e_2 \text{ are the eccentricities of hyperbolas}\} = (\alpha, \beta)\), and \(\{a \in \mathbb{R} : e_1 \text{ and } e_2 \text{ are the eccentricities of an ellipse and a hyperbola, respectively}\} = (\gamma, \infty)\). Then \(\alpha^2 + \beta^2 + \gamma^2\) is equal to:JEE Mains 2026 Hard