Question

Find the possible values of x if standard deviation of the numbers 2, 3, 2x and 11 is 3.5.

Answer 1

Given: Standard Deviation, σ = 3.5

and Numbers are 2, 3, 2x, 11

We know that,

=> 12.25 = 1/16[16 + 8x + x² + 4 + 4x + x² + 64 - 48x + 9x² + 196 - 28x + x²]

⇒ 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

⇒ x = 7/3

Hence, the possible value of x are 7/3 and 3

Comments

This is incorrect answer. The correct answer is x = 3, 7/3.

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plz check answer again.