Question

3. Use the formula given above to calculate the approximate standard deviation of the distribution of sample means.

Answer 1

Answer:

$s_{x}=\frac{s}{\sqrt{n}}\Rightarrow s_{x}=\frac{6.27}{\sqrt{10}}\Rightarrow s_{x}\approx 1.984$

Step-by-step explanation:

(Retrieved data)

1) In this case we have this sample:

$12,5,2,4,1,4,18,10,1,16.$

2) To calculate the Standard Deviation of the Sample we can find it by plugging in the Mean, etc. (Check the Table Below):

$s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^{2}}\Rightarrow s=\sqrt{\frac{354,1}{9}}\Rightarrow s\approx 6.27$

3) Finally, we come to this question. What this question wants to know is the Standard Error of the Mean. Despite some confusion, this in fact means "The Standard Deviation of the Sample Distribution of Some Statistic", by some "statistic"= the Mean, median, Correlation, etc.. It informs us how much error can we expect.

In this case,

$s_{x}=\frac{s}{\sqrt{n}}\Rightarrow s_{x}=\frac{6.27}{\sqrt{10}}\Rightarrow s_{x}\approx 1.984$