Standard Deviation of the Sample Mean

Standard Deviation for n=25.

Click "clear lower 3" and change the sample size to 25.

Look at the left side of the blue histogram. Notice that it gives the standard deviation of the sample means (given in red). What is this standard deviation?

	a)	10
	b)	16
	c)	about 3.0
	d)	about 2.0
	e)	about 2.5
	f)	about 1.0
Please select an answerIncorrect, look at the spread of the sample means (blue histogram) not the population (black histogram).Incorrect, look at the spread of the sample means (blue histogram) not sample size.Incorrect, look at the spread of the sample means (blue histogram).Correct. The spread of the sample means is around 2.0 which is 1/5 the spread of the population.Incorrect, look at the spread of the sample means (blue histogram). Be sure you are taking samples of 25 instead of 16.Incorrect, look at the spread of the sample means (blue histogram).

Standard Deviation for n=36.

Click "clear lower 3" and change the sample size to 36.

Look again at the left side of the blue histogram. Notice that it gives the standard deviation of the sample means (given in red). What is this standard deviation?

	a)	10
	b)	16
	c)	about 4.68
	d)	about 7.34
	e)	about 2.54
	f)	about 1.67
Please select an answerIncorrect, look at the spread of the sample means (blue histogram) not the population (black histogram).Incorrect, look at the spread of the sample means (blue histogram) not sample size.Incorrect, it is not 4.68. Look again.Incorrect, it is not 7.34. Look againIncorrect, it is not 2.54. Look again Correct. The spread of the sample means is around 1.67 which is 1/6 the spread of the population.

Standard Deviation for n=100.

Click "clear lower 3" and change the sample size to 100.

Look again at the left side of the blue histogram. Notice that it gives the standard deviation of the sample means (given in red). What is this standard deviation?

	a)	10
	b)	16
	c)	about 5.68
	d)	about 3.34
	e)	about 1.67
	f)	about 1.00
Please select an answerIncorrect, look at the spread of the sample means (blue histogram) not the population (black histogram).Incorrect, look at the spread of the sample means (blue histogram) not sample size.Incorrect, it is not 5.68. Look again.Incorrect, it is not 3.34. Look againIncorrect, it is not 1.67. Look again Correct. The spread of the sample means is around 1.00 which is 1/10 the spread of the population.

Recap the results

Review the questions you just answered. Match each of the sample sizes to the appropriate relationship between the sample standard deviation and the population standard deviation.

a)	the sample standard deviation is about 1/10 as big as the population standard deviation.	Choose... n=16 n=25 n=36 n=100
b)	the sample standard deviation is about 1/6 as big as the population standard deviation.	Choose... n=16 n=25 n=36 n=100
c)	the sample standard deviation is about 1/5 as big as the population standard deviation.	Choose... n=16 n=25 n=36 n=100
d)	the sample standard deviation is about 1/4 as big as the population standard deviation.	Choose... n=16 n=25 n=36 n=100
Correct. Notice that the proportion is 1 divided by the square root of the sample size.Incorrect. Check your answers again.Your answer has been saved.