The mean of the sample distribution of x̄ (also called the mean of x̄) is the mean of all possible sample means.

In the lesson on sample distribution, we obtained the following sample distribution of x̄.

x P (x̄)
83.33 0.10
85 0.20
85.66 0.20
86.66 0.10
87.33 0.20
89 0.20
∑P (x̄) = 1

What if we try to find the mean of all of these sample means? This mean value is also called the mean value of x̄ for short.

Mean = Σx̄P (x̄) = 83.33 × 0.10 + 85 × 0.20 + 85.66 × 0.20 + 86.66 × 0.10 + 87.33 × 0.20 + 89 × 0.20

Mean = 8.333 + 17 + 17.132 + 8.666 + 17.466 + 17.8

Mean = 86.397 and 86.397 rounded to the nearest tenth is 86.4

Remember, however, that in the population distribution lesson we calculated the population mean and found that μ = 86.4.

As you can see, the mean of the sample distribution of x̄ is equal to the population mean.

It is then appropriate to use the symbol μ for the mean of the sample distribution of x̄ since it is equal to the population mean.

For the sake of clarity, however, we can use μx

μx = Mean of the sample distribution of x̄

We write μx = μ

The sample mean x̄ can also be used as an estimate of the population mean μ. are designated

If μx = μ, we say that x̄ is an unbiased estimator.



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