Answer to Question #344920 in Statistics and Probability for GAB

Question

A group of 8 students in your class having the weight of 50, 52, 53, 54, 56, 57, 58, and 60.

1.Calculate the standard deviation of the sampling distribution of the sample means. Compare this to the standard deviation of the population. 

Answer 1

standard deviation of the sampling distribution of the sample means:

$S=\sqrt{\frac{\sum(x_i-\=x)^2}{n-1}}$

$\=x=\frac{50+52+53+54+56+57+58+60}8=55$

$S=\sqrt{\frac{(50-55)^2+(52-55)^2+(53-55)^2+(54-55)^2+(56-55)^2+(57-55)^2+(58-55)^2+(60-55)^2}{7}}=\sqrt{11.143}=3.34$

standard deviation of the population:

$\sigma=\sqrt{\frac{\sum(x_i-\mu)^2}{N}}\\=\sqrt{\frac{78}{8}}=3.12$

As we can see, the standard deviation of the population is less than the standard deviation of the sampling distribution of the sample means due to the differences in formulas: in standard deviation of the population we divide by N (count of values in population), while in standard deviation of the sampling distribution of the sample means we divide by n-1 (count of values in sample-1).