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statistics · worked example

Solve Standardabweichung von {1, 2, 3, 4, 5} = = √2 ≈ 1.414

Method: Standardabweichung der Grundgesamtheit. Verified step-by-step solution with our free AI math solver.
Problem

σ, {1,2,3,4,5}\sigma,\ \{1, 2, 3, 4, 5\}

Step-by-step solution

  1. Berechne den Mittelwert: xˉ=1+2+3+4+55=3\bar{x} = \frac{1+2+3+4+5}{5} = 3.

  2. Abweichungen vom Mittelwert: −2,−1,0,1,2-2, -1, 0, 1, 2.

  3. Quadrierte Abweichungen: 4,1,0,1,44, 1, 0, 1, 4. Summe = 1010.

  4. Varianz der Grundgesamtheit: σ2=105=2\sigma^2 = \frac{10}{5} = 2.

  5. Standardabweichung: σ=2≈1.414\sigma = \sqrt{2} \approx 1.414.

Answer

σ=2≈1.414\sigma = \sqrt{2} \approx 1.414

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