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Math Asked by a SnapAndSolve user · about 1 hour ago

What is the standard deviation for the set of data {6, 7, 8, 9, 10}?

18. What is the standard deviation for the set of data {6, 7, 8, 9, 10}? Find the standard deviation by completing the table.

Answer

Step 1: Calculate the mean (x̄) of the data set.

The mean is given as x̄ = 4.

Step 2: Complete the table by calculating x - x̄ and (x - x̄)² for each data point.

  1. For x = 6: x - x̄ = 6 - 4 = 2; (x - x̄)² = 2² = 4
  2. For x = 7: x - x̄ = 7 - 4 = 3; (x - x̄)² = 3² = 9
  3. For x = 8: x - x̄ = 8 - 4 = 4; (x - x̄)² = 4² = 16
  4. For x = 9: x - x̄ = 9 - 4 = 5; (x - x̄)² = 5² = 25
  5. For x = 10: x - x̄ = 10 - 4 = 6; (x - x̄)² = 6² = 36

Step 3: Calculate the sum of (x - x̄)².

Σ(x - x̄)² = 4 + 9 + 16 + 25 + 36 = 90

Step 4: Calculate the variance (s²).

s² = Σ(x - x̄)² / n = 90 / 5 = 18

Step 5: Calculate the standard deviation (s).

s = √s² = √18 ≈ 4.24

The standard deviation for the set of data {6, 7, 8, 9, 10} is approximately 4.24.

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