If the standard deviation of the numbers 2, 3, 2x, 11 is 3.5, calculate the possible values of x.

Question

Philoid · Accepted Answer

Given: Standard Deviation, σ = 3.5

and Numbers are 2, 3, 2x, 11

We know that,

⇒ 12.25 × 16 = 280 – 64x + 12x²

⇒ 196 = 280 – 64x + 12x²

⇒ 12x² – 64x + 280 – 196 = 0

⇒ 12x² – 64x + 84 = 0

⇒ 3x² – 16x + 21 = 0

⇒ 3x² – 9x – 7x + 21 = 0

⇒ 3x(x – 3) – 7(x – 3) = 0

⇒ (3x – 7)(x – 3) = 0

Putting both the factors equal to 0, we get

3x – 7 = 0 and x – 3 = 0

⇒ 3x = 7 and x = 3