Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Find the sample variance and standard deviation.?

(22, 10, 4, 6, 11)

A. s^2=

B. s=

1 Answer

Relevance
  • Find the mean:

    (4 + 6 + 10 + 11 + 22) / 5 =>

    (10 + 10 + 33) / 5 =>

    53 / 5 =>

    10.6

    Now, find the difference between each term and the mean

    10.6 - 4 = 6.6

    10.6 - 6 = 4.6

    10.6 - 10 = 0.6

    10.6 - 11 = -0.4

    10.6 - 22 = -11.4

    Square each difference and sum those squares

    6.6^2 + 4.6^2 + 0.6^2 + (-0.4)^2 + (-11.4)^2 =>

    43.56 + 21.16 + 0.36 + 0.16 + 129.96 =>

    195.2

    Find the mean of that sum

    195.2 / 5 =>

    ‭39.04‬

    That's the variance.  The standard deviation will be the square root of that

    39.04 =>

    3904 / 100 =>

    976 / 25 =>

    16 * 61 / 25

    sqrt(16 * 61 / 25) =>

    4 * sqrt(61) / 5 =>

    ‭6.2481997407253235153037781886073‬

    6.248, roughly

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