Question:
The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1,3 and 8, then a ratio of other two observations is :
$4: 9$
$6: 7$
$5: 8$
$10: 3$
Correct Option: 1
Solution:
Let two observations are $\mathrm{x}_{1}$ \& $\mathrm{x}_{2}$
mean $=\frac{\sum \mathrm{x}_{\mathrm{i}}}{5}=5 \Rightarrow 1+3+8+\mathrm{x}_{1}+\mathrm{x}_{2}=25$
$\Rightarrow x_{1}+x_{2}=13$ ..................(1)
variance $\left(\sigma^{2}\right)=\frac{\sum x_{i}^{2}}{5}-25=9.20$
$\Rightarrow \sum x_{\mathrm{i}}^{2}=171$
$\Rightarrow x_{1}^{2}+x_{2}^{2}=97$ .................(2)
by (1) \& (2)
$\left(\mathrm{x}_{1}+\mathrm{x}_{2}\right)^{2}-2 \mathrm{x}_{1} \mathrm{x}_{2}=97$
or $x_{1} x_{2}=36$
$\therefore \quad x_{1}: x_{2}=4: 9$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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