JEE Mains · Maths · STD 11 - 13. statistics
The mean and the standard deviation (s.d.) of \(10\) observations are \(20\) and \(2\) resepectively. Each of these \(10\) observations is multiplied by \(\mathrm{p}\) and then reduced by \(\mathrm{q}\), where \(\mathrm{p} \neq 0\) and \(\mathrm{q} \neq 0 .\) If the new mean and new s.d. become half of their original values, then \(q\) is equal to
- A \(-20\)
- B \(10\)
- C \(-10\)
- D \(-5\)
Answer & Solution
Correct Answer
(A) \(-20\)
Step-by-step Solution
Detailed explanation
\(20 \mathrm{p}-\mathrm{q}=10\ldots(i)\) and \(2|p|=1 \Rightarrow p=\pm \frac{1}{2}\ldots(ii)\) so, \(\mathrm{p}=-\frac{1}{2}\) and \(\mathrm{q}=-20\)
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 \(S_{1}: x^{2}+y^{2}=9\) and \(S_{2}:(x-2)^{2}+y^{2}=1\). Then the locus of center of a variable circle \(S\) which touches \(S_{1}\) internally and \(S_{2}\) externally always passes through the points :JEE Mains 2021 Hard
- Let \(f : R \rightarrow R\) be a differentiable function such that \(f^{\prime}(x)+f(x)=\int \limits_0^2 f(t) d t\). If \(f(0)=e^{-2}\), then \(2 f (0)- f (2)\) is equal to \(.........\).JEE Mains 2023 Hard
- Let \( f, \mathrm{~g}: \mathrm{R} \rightarrow \mathrm{R}\) be defined as : \(f(\mathrm{x})=|\mathrm{x}-1|\) and \(g(x)=\left\{\begin{array}{cc}\mathrm{e}^{\mathrm{x}}, & \mathrm{x} \geq 0 \\ \mathrm{x}+1, & \mathrm{x} \leq 0\end{array}\right.\). Then the function \(f(\mathrm{~g}(\mathrm{x}))\) isJEE Mains 2024 Hard
- The axis of a parabola is the line \(y=x\) and its vertex and focus are in the first quadrant at distances \(\sqrt{2}\) and \(2 \sqrt{2}\) units from the origin, respectively. If the point \((1, \mathrm{k})\) lies on the parabola, then a possible value of \(k\) is :-JEE Mains 2025 Easy
- If a complex number \(z\) statisfies the equation \(x + \sqrt 2 \,\,\left| {z + 1} \right|\,+ \,i\, = \,0,\) then \(\left| z \right|\) is equal toJEE Mains 2013 Hard
- Let \(A\) be a \(3 \times 3\) real matrix such that \(A^2(A-2 I)-\) \(4(\mathrm{~A}-\mathrm{I})=\mathrm{O}\), where I and O are the identity and null matrices, respectively. If \(A^5=\alpha A^2+\beta A+\gamma I\), where \(\alpha, \beta\) and \(\gamma\) are real constants, then \(\alpha+\beta+\gamma\) is equal to:JEE Mains 2025 Medium
More PYQs from JEE Mains
- The set of all real values of \(\lambda\) for which the function \(f(x)=\left(1-\cos ^{2} x\right) \cdot(\lambda+\sin x)\) \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right),\) has exactly one maxima and exactly one minima, isJEE Mains 2020 Hard
- If the vector \(\vec b = 3\hat j + 4\hat k\) is written as the sum of a vector \({\vec {b_1}}\) , parallel to \(\vec a = \hat i + \hat j\) and a vector \({\vec {b_2}}\) , perpendicular to \(\vec a\) , then \({\vec {b_1}} \times {\vec {b_2}}\) is equal toJEE Mains 2017 Hard
- Given \(\frac{{b + c}}{{11}} = \frac{{c + a}}{{12}} = \frac{{a + b}}{{13}}\) for a \(\Delta ABC\) with usual nation. If \(\frac{{\cos \,A}}{\alpha } = \frac{{\cos \,\beta }}{\beta } = \,\frac{{\cos \,C}}{\gamma }\), then the ordered tried \(\left( {\alpha ,\beta ,\gamma } \right)\) has a valueJEE Mains 2019 Hard
- The value of \(-{ }^{15} C _{1}+2 .{ }^{15} C _{2}-3 .{ }^{15} C _{3}+\ldots \ldots\) \(-15 .{ }^{15} C _{15}+{ }^{14} C _{1}+{ }^{14} C _{3}+{ }^{14} C _{5}+\ldots .+{ }^{14} C _{11}\) isJEE Mains 2021 Hard
- If \(f\left( x \right) = \frac{{2 - x\,\cos \,x}}{{2 + x\,\cos \,x}}\) and \(g\left( x \right) = {\log _e}\,x\), \(\left( {x > 0} \right)\) then the value of the integral \(\int\limits_{\frac{{ - \pi }}{4}}^{\frac{\pi }{4}} {g\left( {f\left( x \right)} \right)} dx\) isJEE Mains 2019 Hard
- If the equations \({x^2} + 2x + 3 = 0\) and \(a{x^2} + bx + c = 0,a,b,c \in R\) have a common root ,then \(a:b:c = \) .. . .JEE Mains 2013 Easy