5 students of a class have an average height $150 \mathrm{~cm}$ and variance $18 \mathrm{~cm}^{2}$. A new student, whose height is $156 \mathrm{~cm}$, joined them. The variance (in $\mathrm{cm}^{2}$ ) of the height of these six students is:
22
20
16
18
Correct Option: , 2
Given $\vec{x}=\frac{\Sigma x_{i}}{5}=150$
$\Rightarrow \sum_{i=1}^{5} x_{i}=750$ $\ldots \ldots(\mathrm{i})$
$\frac{\sum \mathrm{x}_{\mathrm{i}}^{2}}{5}-(\overrightarrow{\mathrm{x}})^{2}=18$
$\frac{\sum x_{i}^{2}}{5}-(150)^{2}=18$
$\Sigma \mathrm{x}_{\mathrm{i}}^{2}=112590$ ....(ii)
Given height of new student
$x_{6}=156$
Now, $\quad \vec{x}_{\text {new }}=\frac{\sum_{i=1}^{6} x_{i}}{6}=\frac{750+156}{6}=151$
Also, New variance $=\frac{\sum_{i=1}^{6} x_{i}^{2}}{6}-\left(\bar{x}_{\text {new }}\right)^{2}$
$=\frac{112590+(156)^{2}}{6}-(151)^{2}$
$=22821-22801=20$
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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,