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charizvalerie14
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Tyro
Asked: 2021-04-13T01:51:27+00:00 In: ,

Sampling Distribution

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A population N=5 consists of the following values: 9, 11, 13, 15, and 17. Find the mean, variance, and standard deviation using a random variable of size n=3

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  2. acedstud
    This answer was edited.

    In sampling distribution, the population mean is equal to the mean of the distribution of the samples of size n. That is, \mu=\mu_{\bar{x}}.

    Here, \mu=\dfrac{9+11+13+15+17}{5}=\dfrac{65}{5}=13.

    Also, the variance of the distribution of samples of size n is given by \sigma^2_{\bar{x}}=\dfrac{\sigma^2}{n}.

    Here,

    \sigma^2=\dfrac{(9-13)^2+(11-13)^2+(13-13)^2+(15-13)^2+(17-13)^2}{5}=\dfrac{16+4+0+4+16}{5}

    =\dfrac{40}{5}=8.

    Thus, \sigma^2_{\bar{x}}=\dfrac{8}{5}=1.6.

    Also, the standard deviation is the square root of the variance, hence, \sigma_{\bar{x}}=\sqrt{\sigma^2_{\bar{x}}}=\sqrt{1.6}\approx1.265.

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