NIMCET 2015 Question Paper with solutions

© examsiri.com

Question : 14 of 120

Marks: +1, -0

If the mean deviation of the numbers 1, 1+d, 1+2d, ..., 1+100d from their mean is 255, then the value of ‘d’ is;

20.0
10.1
20.2
10.0

Solution:

Mean

={1+1+d+1+2d+. . .+1+100d}/{101}

Mean

={101+d(1+2+3+. . .+100)}/{101}

⇒Mean

={101+d({100×101}/{2})}/{101}={101(1+50d)}/{101}=50d+1

⇒ MD

(\ov{x})={Σ|x_1-\ov{x}|}/x

MD

\ov{x}={|1-50d-1|+|1+d-50d-1|+..|1+100d-50d-1|}/101

⇒225={(50d+49d+....d)+(d+2d+3d....50d)}/101

⇒225={2d(1+23+....+50)}/101

⇒225={2d(50×51)}/{2×101}\;\;⇒\;\;\;d={22×101}/{50×51}=8.91

None option is correct

© examsiri.com

Go to Question:

Prev Question

Next Question