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