JEE Mains · Maths · STD 11 - 13. statistics
lf the mean deviation of the numbers \(1, 1 + d, . . . ,1 + 100d\) from their mean is \(255,\) then a value of \(d\) is
- A \(10.1\)
- B \(5.05\)
- C \(20.2\)
- D \(10\)
Answer & Solution
Correct Answer
(A) \(10.1\)
Step-by-step Solution
Detailed explanation
\(\bar x = \frac{1}{{101}}\left[ {1 + \left( {1 + d} \right) + \left( {1 + 2d} \right).....\left( {1 + 100d} \right)} \right]\) \( = \frac{1}{{101}} \times \frac{{101}}{2}\left[ {1 + \left( {1 + 100d} \right)} \right] = 1 + 50d\) mean deviation from mean…
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 \(\mathrm{a}=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+\ldots\), \(\mathrm{b}=1+\frac{{ }^1 \mathrm{C}_0+{ }^1 \mathrm{C}_1}{1 !}+\frac{{ }^2 \mathrm{C}_0+{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_2}{2 !}+\frac{{ }^3 \mathrm{C}_0+{ }^3 \mathrm{C}_1+{ }^3 \mathrm{C}_2+{ }^3 \mathrm{C}_3}{3 !}+\ldots\) Then \(\frac{2 b}{a^2}\) is equal to ...........JEE Mains 2024 Hard
- The product of all the rational roots of the equation \(\left(x^2-9 x+11\right)^2-(x-4)(x-5)=3\), is equal toJEE Mains 2025 Medium
- If \(\left(2\alpha+1, \alpha^2-3\alpha, \dfrac{\alpha-1}{2}\right)\) is the image of \((\alpha, 2\alpha, 1)\) in the line \(\dfrac{x-2}{3}=\dfrac{y-1}{2}=\dfrac{z}{1}\), then the possible value(s) of \(\alpha\) is (are)JEE Mains 2026 Hard
- If \(z_{1}, z_{2}\) are complex numbers such that \(\operatorname{Re}\left(z_{1}\right)=\left|z_{1}-1\right|, \operatorname{Re}\left(z_{2}\right)=\left|z_{2}-1\right|\) and \(\arg \left(z_{1}-z_{2}\right)=\frac{\pi}{6},\) then \(\operatorname{Im}\left(z_{1}+z_{2}\right)\) is equal toJEE Mains 2020 Hard
- Let the circle \(C_1: x^2+y^2-2(x+y)+1=0\) and \(C_2\) be a circle having centre at \((-1,0)\) and radius \(2\) . If the line of the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) intersects the \(\mathrm{y}\)-axis at the point \(\mathrm{P}\), then the square of the distance of \(\mathrm{P}\) from the centre of \(\mathrm{C}_1\) is :JEE Mains 2024 Hard
- If the image of the point \(P(1, 2, a)\) in the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-z}{2}\) is \(Q(5,b,c)\), then \(a^{2}+b^{2}+c^{2}\) is equal toJEE Mains 2026 Hard
More PYQs from JEE Mains
- The set of all values of \(\lambda\) for which the equation \(\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda\)JEE Mains 2023 Hard
- The minimum value of the function \(f(x)=\int \limits_0^2 e^{|x-t|} d t\) isJEE Mains 2023 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
- Let the mean and variance of four numbers \(3,7, x\) and \(y(x>y)\) be \(5\) and \(10\) respectively. Then the mean of four numbers \(3+2 \mathrm{x}, 7+2 \mathrm{y}, \mathrm{x}+\mathrm{y}\) and \(x-y\) is ..... .JEE Mains 2021 Hard
- Let \((\alpha, \beta, \gamma)\) be mirror image of the point \((2,3,5)\) in the line \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\). Then \(2 \alpha+3 \beta+4 \gamma\) is equal toJEE Mains 2024 Medium
- The students \(S _{1}, S _{2}, \ldots \ldots, S _{10}\) are to be divided into \(3\) groups \(A , B\) and \(C\) such that each group has at least one student and the group \(C\) has at most \(3\) students. Then the total number of possibilities of forming such groups is ........ .JEE Mains 2021 Hard