std devn and std error of sampling

CFA Level I
#1

Std error of sampling is the std devn for a sample of size n. Two questions- 1. How is it that std devn for n=1, is popn std devn…and std devn for increasing n is lower…std devn for increasing n is lower makes sense, but if we have only one element in the sample, why will the std devn for the sample equal the popn std devn. And for increasing n it is less than popn std devn. Acc to me popn std devn is the variability that is attained by taking max possible elements into account. Then why is it that for n=1, popn std d3vn is equal to sample std devn? This is weird. What am I missing?

#2

If n=1 it means there is only one item in the sample ==> sample size = size of the population

SE = s/n that is sample std deviation divided by the size of the sample and so SE of a sample whose size is 1 is s/1 = s. As sample size and population are same (n=1), s is also equal to population std deviation.

Is my understanding correct?

#3

How is it possible that a popn has only one element. I think you got it wrong there.

#4

Removed

#5

I think you’re confusing some ideas here.

Standard error of the estimate does not relate the standard deviation of the population to the standard deviation of the sample. Standard error of the estimate relates the standard deviation for a single observation to the standard deviation for the mean of several observations. If you have only one observation (i.e., sample size n = 1), then the standard deviation for that observation is the same as the standard deviation for the mean because that observation _ is _ the mean, and its volatility is the mean’s volatility.

#6

Thanks a lot S2000magician for the clarification. After reading your explantion, I realize the need for me to use the correct terms in statistics

Thanks blackjack21 for raising this doubt. Very useful

#7

Then, why is it called popn std devn divided by sq root of n. What is the “popn” here?

#8

If you know the standard deviation of the population, then you use that in the formula for standard error (there’s no need to estimate a number you already know); if you don’t know the standard deviation of the population, you use the standard deviation of the sample.

That notwithstanding, standard deviation (whether population or sample) gives you the dispersion of a single observation within a sample; standard error gives you the dispersion of the mean of the sample.

#9

Great. I didn’t know about the concept of std error. Brilliant!