Standard deviation and standard error are, generally speaking, measures of varia

Question

Standard deviation and standard error are, generally speaking, measures of variation. a. Explain what each measures more specifically. b. If you were to plot the standard deviations of a normally distributed population on a histogram, what would it look like? c. If you were to plot the standard errors of samples taken from on a normally distributed population on a histogram, what would it look like? d. Suppose I gave you 2 numbers in a problem: 4.5 and 6.7. One is the standard deviation and one is the standard error. Do you have enough information to tell me which is which? Why or why not?

Explanation / Answer

Answer to the questions:

a.

The SD (standard deviation) quantifies scatter — how much the values vary from one another.

The Standard error of the mean is the relationship between the dispersion of individual observations around the population mean (the standard deviation), and the dispersion of sample means around the population mean (thestandard error).

b. It will look like a bell curve

c. It will still look like a bell curve, more flattish though, more fatter tails, and centered around the same mean and with a standard deviation equal to the standard error which is essetinally a standard deviation of population divided by sqrt(n)

d. SInce we have proven above that std error will be stdev/sqrt(n) , we have smaller value for std error. i.e. 6.7 is std deviation and 4.5 is standard error.

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