Multiple choice

Standard deviation of four observations $-1, 0, 1$ and k is $\sqrt{5}$ then k will be?

  1. $2\sqrt{6}$
  2. $1$
  3. $2$
  4. $\sqrt{6}$
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AI explanation

The mean of the four observations negative 1, 0, 1, and k is calculated as k divided by 4. The variance formula is the sum of squared deviations divided by the number of items, which gives the equation ((negative 1 minus k/4) squared plus (0 minus k/4) squared plus (1 minus k/4) squared plus (k minus k/4) squared) divided by 4 equals 5. Solving this yields k squared plus 4 equals 20, meaning k squared equals 24. Taking the square root gives k equal to 2 multiplied by the square root of 6.

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