Question

If the mean deviation of number 1, 1 + d, 1 + 2d, ..., 1 + 100d from their mean is 255, then d is equal to ______.

Options

• 10.0

• 20.0

• 10.1

• 20.2

Answer 1

If the mean deviation of number 1, 1 + d, 1 + 2d, ..., 1 + 100d from their mean is 255, then d is equal to 10.1.

Explanation:

We know that,

`overlinex = "Sum of quantities"/n`

= `(n/2 (a + 1))/n`

= `1/2 (1 + 1 + 100d)`

= 1 + 50d

∴ Mean deviation = `1/n sum |x_i - overlinex|`

`\implies` 255 = `1/101 [50d + 49d + 48d + ... + d + 0 + d + ... + 50d]`

= `(2d)/101 ((50 xx 51)/2)`

∴ d = `(255 xx 101)/(50 xx 51)` = 10.1