JEE Mains · Maths · STD 11 - 13. statistics
The mean of the numbers \(a, b, 8,5,10\) is \(6\) and their variance is \(6.8\). If \(M\) is the mean deviation of the numbers about the mean, then \(25\; M\) is equal to
- A \(60\)
- B \(55\)
- C \(50\)
- D \(75\)
Answer & Solution
Correct Answer
(A) \(60\)
Step-by-step Solution
Detailed explanation
\(\sigma^{2}=\frac{\sum\limits_{i=1}^{5}\left(x_{i}-\bar{x}\right)^{2}}{n}\) Mean \(=6\) \(\frac{a+b+8+5+10}{5}=6\) \(a+b=7\) \(b=7-a\) \(6.8=\frac{(a-6)^{2}+(b-6)^{2}+(8-6)^{2}+(5-6)^{2}+(10-6)^{2}}{5}\) \(34=(a-6)^{2}+(7-a-6)^{2}+4+1+18\) \(a^{2}-7 a+12=0 \Rightarrow a=4\) or…
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
- \(\lim \limits_{x \rightarrow \frac{\pi}{2}}(\tan ^{2} x((2 \sin ^{2} x+3 \sin x+4)^{\frac{1}{2}}\) \(-(\sin ^{2} x+6 \sin x+2)^{\frac{1}{2}}))\) is equal toJEE Mains 2022 Hard
- The constant term in the expansion of \(\left(2 x+\frac{1}{x^7}+3 x^2\right)^5 \text { is }........\).JEE Mains 2023 Hard
- If \(\frac{{dy}}{{dx}} + y\tan x = \sin 2x\) and \(y(0)\,=1\) , then \(y(\pi)\) is equal toJEE Mains 2014 Hard
- The sum of all values of \( \alpha \), for which the shortest distance between the lines \( \frac{x+1}{\alpha}=\frac{y-2}{-1}=\frac{z-4}{-\alpha} \) and \( \frac{x}{\alpha}=\frac{y-1}{2}=\frac{z-1}{2\alpha} \) is \( \sqrt{2} \), isJEE Mains 2026 Medium
- If \(\sum\limits_{ k =1}^{31}\left({ }^{31} C _{ k }\right)\left({ }^{31} C _{ k -1}\right)-\sum\limits_{ k =1}^{30}\left({ }^{30} C _{ k }\right)\left({ }^{30} C _{ k -1}\right)=\frac{\alpha(60 !)}{(30 !)(31 !)}\) Where \(\alpha \in R\), then the value of \(16 \alpha\) is equal toJEE Mains 2022 Hard
- The value of \((0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots . to \infty\right)}\) is equal toJEE Mains 2020 Hard
More PYQs from JEE Mains
- The function \(f(x)=\frac{4 x^{3}-3 x^{2}}{6}-2 \sin x+(2 x-1) \cos x\)JEE Mains 2021 Hard
- If \(f(a+b+1-x)=f(x),\) for all \(x,\) where \(a\) and \(b\) are fixed positive real numbers, then \(\frac{1}{a+b} \int\limits_{a}^{b} x(f(x)+f(x+1)) d x\) is equal toJEE Mains 2020 Hard
- If \(1+\frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}+\frac{5-2 \sqrt{6}}{18}+\frac{9 \sqrt{3}-11 \sqrt{2}}{36 \sqrt{3}}+\frac{49-20 \sqrt{6}}{180}+\ldots\) upto \(\infty=2\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)\), where \(a\) and \(b\) are integers with \(\operatorname{gcd}(a, b)=1\), then \(11 a+18 b\) is equal to ...............JEE Mains 2024 Hard
- Let \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) be the solution curve of the differential equation, \(\quad\left(y^{2}-x\right) \frac{d y}{d x}=1\) satisfying \(\mathrm{y}(0)=1 .\) This curve intersects the \(\mathrm{x}\) -axis at a point whose abscissa isJEE Mains 2020 Hard
- The number of common tangents to the circles \({x^2} + {y^2} - 4x - 6y - 12 = 0\) and \({x^2} + {y^2} + 6x + 18y + 26 = 0\) isJEE Mains 2015 Hard
- The sum \(\sum\limits_{k=1}^{20}(1+2+3+\ldots+k)\) isJEE Mains 2020 Medium