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Which of the following formula is used in calculating standard deviation?

Mathematics

ScanSolve AI Answer

Answer

C

Step-by-step solution

6 steps
  1. The standard deviation for a population of NN data points is given by the formula

    σ=∑i=1N(xi−xˉ)2N,\sigma = \sqrt{\dfrac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N}},

    where xˉ\bar{x} is the mean xˉ=∑xiN\bar{x} = \dfrac{\sum x_i}{N}.

  2. Compare with option A

    xˉ−xN\sqrt{\dfrac{\bar{x} - x}{\sqrt{N}}}.
    This lacks the sum ∑\sum, squared differences (xi−xˉ)2(x_i - \bar{x})^2, and has incorrect denominator N\sqrt{N}. Incorrect.

  3. Compare with option B

    ∑(xi−xˉ)N\sqrt{\dfrac{\sum (x_i - \bar{x})}{N}}.
    This averages the differences (xi−xˉ)(x_i - \bar{x}) without squaring them. Incorrect (this resembles mean absolute deviation).

  4. Compare with option C

    ∑(xi−xˉ)2N\sqrt{\dfrac{\sum (x_i - \bar{x})^2}{N}}.
    This matches the standard deviation formula exactly. Correct.

  5. Compare with option D

    ∑(xi−xˉ)2N\sqrt{\dfrac{\sum (x_i - \bar{x})^2}{N}} (OCR artifacts like "10 szu" likely irrelevant; appears identical to C, but context suggests possible sample variant—however, standard population uses NN).
    Option C is the clear match.

  6. Compare with option E

    (x−xˉ)2N\sqrt{\dfrac{(x - \bar{x})^2}{N}}.
    Lacks the sum ∑\sum over all data points. Incorrect.

    C

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