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What is the sample standard deviation for the following numbers: 60, 93, 1, 42, 93?

Please format the answer to 2 decimal places.

Answer :

To find the Sample Standard Deviation of the numbers 60, 93, 1, 42, and 93, follow these steps:

  1. Calculate the Mean: Add up all the numbers and divide by the number of items.

    [tex]\text{Mean} = \frac{60 + 93 + 1 + 42 + 93}{5} = \frac{289}{5} = 57.8[/tex]

  2. Find the Deviations from the Mean: Subtract the mean from each number to get the deviation for each value.

    • [tex]60 - 57.8 = 2.2[/tex]
    • [tex]93 - 57.8 = 35.2[/tex]
    • [tex]1 - 57.8 = -56.8[/tex]
    • [tex]42 - 57.8 = -15.8[/tex]
    • [tex]93 - 57.8 = 35.2[/tex]

  3. Square Each Deviation: Square the deviations to eliminate negative values.

    • [tex](2.2)^2 = 4.84[/tex]
    • [tex](35.2)^2 = 1239.04[/tex]
    • [tex](-56.8)^2 = 3225.44[/tex]
    • [tex](-15.8)^2 = 249.64[/tex]
    • [tex](35.2)^2 = 1239.04[/tex]

  4. Calculate the Variance: Find the average of these squared deviations. Since this is a sample, divide by [tex]n-1[/tex], where [tex]n[/tex] is the number of data points.

    [tex]\text{Variance} = \frac{4.84 + 1239.04 + 3225.44 + 249.64 + 1239.04}{5 - 1} = \frac{5957}{4} = 1489.25[/tex]

  5. Find the Sample Standard Deviation: Take the square root of the variance.

    [tex]\text{Sample Standard Deviation} = \sqrt{1489.25} \approx 38.60[/tex]

Therefore, the Sample Standard Deviation of the numbers 60, 93, 1, 42, and 93 is approximately 38.60.

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