Understanding Standard Deviation for Sample Means in Statistics

In summary, the conversation discusses the calculation of standard deviation for a sample mean and the reason for dividing the population standard deviation by the square root of n. It is explained that the sample variance is defined as the average squared deviation from the mean and is averaged across n observations. It is also noted that when estimating the sample variance, n-1 should be used instead of n. The conversation ends with a thank you for the explanation and appreciation for the help provided.
  • #1
whitaleedee
2
0
Hiya guys, I just have what I'm sure is a simple question about statistics, but I can't seem to find it anywhere ...

I was wondering, when finding the standard deviation of a sample mean, why do you divide the population standard deviation by the square root of n? I'm not really sure why they took the square root ... if anyone could help, I'd really appreciate it :biggrin:

Thanks so much!
 
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  • #2
The short answer is because sample variance is defined as this. And the heuristic explanation for the sample variance formula is that the sample variance is the average squared deviation from the mean, so it is being averaged across n observations.
 
  • #3
Slight nitpicking: When you use the sample mean to estimate the sample variance, you should use n-1 not n. If you happen to know the true mean, then you can use n.
 
  • #4
Thanks!

Thank you so much! I was really curious and my AP stats teacher is kind of confused as to what's going on because she hurt herself at the beginning of the year and has been pretty much gone since then, and then refuses to explain why of anything ... I don't think we've actually learned about variance yet, but thanks a lot anyway, I really appreciate it :rofl:
 

What is a sampling distribution?

A sampling distribution is a theoretical distribution that represents all possible samples of a fixed size that can be drawn from a population. It is used to understand the variability of sample statistics and make inferences about the population.

Why is understanding sampling distributions important?

Understanding sampling distributions is important because it allows us to draw conclusions about a population based on a sample. It also helps us to determine the reliability and accuracy of our sample statistics.

How is a sampling distribution different from a population distribution?

A sampling distribution is different from a population distribution in that it represents all possible samples of a fixed size from a population, while a population distribution represents the entire population.

What factors affect the shape of a sampling distribution?

The shape of a sampling distribution is affected by the sample size, the shape of the population distribution, and the sampling method used. As the sample size increases, the sampling distribution approaches a normal distribution, regardless of the shape of the population distribution.

How can sampling distributions be used in hypothesis testing?

Sampling distributions are used in hypothesis testing to determine the likelihood of obtaining a certain sample statistic, given the null hypothesis is true. This allows us to determine the probability of rejecting the null hypothesis and accepting the alternative hypothesis.

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