NIMCET 2014 Mathematics PYQ — The mean deviation from the mean of the AP , is:… | Mathem Solvex | Mathem Solvex
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NIMCET 2014 — Mathematics PYQ
NIMCET | Mathematics | 2014
The mean deviation from the mean of the AP a,a+d,a+2d,...,a+2nd, is:
Choose the correct answer:
A.
n+1nd
B.
2n+1nd
C.
2n+1n+1d
D.
2n+1n(n+1)d
(Correct Answer)
Correct Answer:
2n+1n(n+1)d
Explanation
Concept
The deviation of an observation xi from the mean xˉ, is simply the difference (xˉ−xi).
Arithmetic Progression (AP): The series of numbers where the difference of any two consecutive terms is the same.
The mean of an AP is also the mean of the first and the last terms.
Calculation
The mean of the given AP will be: 2First Term + Last Term
=2(a)+(a+2nd)
=a+nd
Since the terms are equidistant, the magnitude of the deviations of each term less than the mean will be the same as the magnitude of the deviations of the terms more than the mean.
∴Mean deviation=Number of observationsSum of the magnitudes of the deviations
=2n+12×[(n)d+(n−1)d+...+(1)d+(0)d]
=2n+12×[2n(n+1)d]
=2n+1n(n+1)d
Correct Option: 4
Explanation
Concept
The deviation of an observation xi from the mean xˉ, is simply the difference (xˉ−xi).
Arithmetic Progression (AP): The series of numbers where the difference of any two consecutive terms is the same.
The mean of an AP is also the mean of the first and the last terms.
Calculation
The mean of the given AP will be: 2First Term + Last Term
=2(a)+(a+2nd)
=a+nd
Since the terms are equidistant, the magnitude of the deviations of each term less than the mean will be the same as the magnitude of the deviations of the terms more than the mean.
∴Mean deviation=Number of observationsSum of the magnitudes of the deviations
