Question bank/JEE Main/Mathematics
JEE MainMathematics
If the mean deviation of numbers
1, 1 + k, 1 + 2k, 1 + 3k,............, 1 + 100k (k > 0) about their
mean is 255, then k is equal to
Show answer and solution
The numbers 1, 1 + k, 1 + 2k, 1 + 3k,............, 1 + 100k are in
A.P.
Also, Mean = 51st term = (1 + 50k)
∴ Mean deviation about mean = [IMAGE] = [IMAGE] · 2d · (1 + 2 + 3 +...... + 50)
But mean deviation about mean = 255 (Given)
So, we get [IMAGE] k = 255
⇒ k = 10.1
A.P.
Also, Mean = 51st term = (1 + 50k)
∴ Mean deviation about mean = [IMAGE] = [IMAGE] · 2d · (1 + 2 + 3 +...... + 50)
But mean deviation about mean = 255 (Given)
So, we get [IMAGE] k = 255
⇒ k = 10.1
Source: Grass-G / M-01 Mathematics Paper-1.docx
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