A data consists of $\mathrm{n}$ observations:
$\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots \ldots, \mathrm{x}_{\mathrm{n}}$. If $\sum_{\mathrm{i}=1}^{\mathrm{n}}\left(\mathrm{x}_{\mathrm{i}}+1\right)^{2}=9 \mathrm{n} \quad$ and
$\sum_{i=1}^{n}\left(x_{i}-1\right)^{2}=5 n$, then the standard deviation of
this data is :
5
$\sqrt{5}$
$\sqrt{7}$
2
Correct Option: , 2
$\sum\left(x_{i}+1\right)^{2}=9 n$ ..............(1)
$\sum\left(x_{i}-1\right)^{2}=5 n$ ................(2)
$(1)+(2) \Rightarrow \sum\left(x_{1}^{2}+1\right)=7 n$
$\Rightarrow \frac{\sum x_{i}^{2}}{n}=6$
$(1)-(2) \Rightarrow 4 \Sigma x_{i}=4 n$
$\Rightarrow \Sigma x_{\mathrm{i}}=\mathrm{n}$
$\Rightarrow \frac{\Sigma \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}=1$
$\Rightarrow$ variance $=6-1=5$
$\Rightarrow$ Standard diviation $=\sqrt{5}$
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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,