JEE Mains · Maths · STD 11 - 13. statistics
Let the mean of 6 observation \(1,2,4,5, x\) and \(y\) be \(5\) and their variance be \(10\) . Then their mean deviation about the mean is equal to \(........\).
- A \(\frac{10}{3}\)
- B \(\frac{7}{3}\)
- C \(3\)
- D \(\frac{8}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
\(x+y=18\{\because\) mean \(=5\}\) \(10=\frac{1+4+16+25+ x ^2+ y ^2}{6}-25\) \(x ^2+ y ^2=164 \ldots \ldots \text { (ii) }\) By solving \((i)\) and \((ii)\) \(x =8, y =10\) \(\text { M.D. }(\overline{ x })=\frac{\sum\left| x _{ i }-\overline{ x }\right|}{6}=\frac{8}{3}\)
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 the system of linear equations \(x+ ay+z\,= 3\) ; \(x + 2y+ 2z\, = 6\) ; \(x+5y+ 3z\, = b\) has no solution, thenJEE Mains 2018 Hard
- The Coefficient of \(x ^{-6}\), in the expansion of \(\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9\), is \(........\).JEE Mains 2023 Hard
- If in a parallelogram \(ABDC\), the coordinates of \(A, B\) and \(C\) are respectively \((1, 2), (3, 4)\) and \((2, 5)\), then the equation of the diagonal \(AD\) isJEE Mains 2019 Hard
- If \(\frac{1^3+2^3+3^3+\ldots \ldots \text {.upto } n \text { terms }}{1 \cdot 3+2 \cdot 5+3 \cdot 7+\ldots \ldots \text { upto } n \text { terms }}=\frac{9}{5}\), then the value of \(n\) isJEE Mains 2023 Hard
- Two sets \(A\) and \(B\) are as under: \(A = \{ \left( {a,b} \right) \in R \times R:\left| {a - 5} \right| < 1 \,\,and\,\,\left| {b - 5} \right| < 1\} \); \(B = \left\{ {\left( {a,b} \right) \in R \times R:4{{\left( {a - 6} \right)}^2} + 9{{\left( {b - 5} \right)}^2} \le 36} \right\}\) then : . . . . .JEE Mains 2018 Hard
- Let \(f(x)=\min \{[x-1],[x-2], \ldots,[x-10]\}\) where \([ t\) ] denotes the greatest integer \(\leq t\).Then\(\int_{0}^{10} f(x) d x+\int_{0}^{10}(f(x))^{2} d x+\int_{0}^{10}|f(x)| d x\) is equal toJEE Mains 2022 Hard
More PYQs from JEE Mains
- The number of solutions of the equation \(\cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^3 \frac{5 \theta}{2}\) in \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) is :JEE Mains 2025 Medium
- The natural number \(m\), for which the coefficient of \(x\) in the binomial expansion of \(\left( x ^{ m }+\frac{1}{ x ^{2}}\right)^{22}\) is \(1540,\) isJEE Mains 2020 Hard
- Let \(A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]\) If \(A^3=4 A^2-A-21 I\), where I is the identity matrix of order \(3 \times 3\), then \(2 a+3 b\) is equal to :JEE Mains 2024 Hard
- The first of the two samples in a group has \(100\) items with mean \(15\) and standard deviation \(3 .\) If the whole group has \(250\) items with mean \(15.6\) and standard deviation \(\sqrt{13.44}\), then the standard deviation of the second sample is:JEE Mains 2021 Hard
- Let \(a \in Z\) and \([t]\) be the greatest integer \(\leq t\). Then the number of points, where the function \(f(x)=[a\) \(+13 \sin x], x \in(0, \pi)\) is not differentiable, is \(........\).JEE Mains 2023 Hard
- From a lot of \(10\) items, which include \(3\) defective items, a sample of \(5\) items is drawn at random. Let the random variable \(\mathrm{X}\) denote the number of defective items in the sample. If the variance of \(X\) is \(\sigma^2\), then \(96 \sigma^2\) is equal to ....................JEE Mains 2024 Hard