Statistics: sample median, means, s.d. vs sample size

In summary, the conversation discusses the creation of a graph using R to compare the standard deviations of medians, means, and standard deviations for varying sample sizes. The question posed is whether the formula for sample vs. population (sample stat = population stat/sqrt(n)) applies to median and standard deviation in addition to the mean. The program R is mentioned as a tool used in creating the graph.
  • #1
jhson114
82
0
i have a set containing 10000 data. i took 1000 samples of size 4, 16, 64, and 1024 and took the medians, means, and stadard deviations of each size. i graphed them sd of medians vs sample size, sd of mean vs sample size, and sd of s.d. vs sample size. for sample mean, i know from a textbook that:
SD of sample means = population SD / sqrt(sample size n).
But it seems from the graph i created using R, sd of medians and s.d. vs sample size all have the exact same looking graph, which to me suggests that:
SD of sample means, medians, and s.d. = population SD / sqrt(sample size n).
Is this right? it seems a little awkward. any input will be very helpful. thank you
 
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  • #2
graph i created using R
What is R?

More generally, is your question whether the "sample vs. population" formula (sample stat = population stat/sqrt(n)) applies to median and std. dev. in addition to the mean?
 
  • #3
R is just a program language kind of like matlab.

"More generally, is your question whether the "sample vs. population" formula (sample stat = population stat/sqrt(n)) applies to median and std. dev. in addition to the mean?"

This is exact what I'm asking.
 

1. What is a sample median?

A sample median is the middle value of a set of data when arranged in ascending or descending order. It represents the 50th percentile or the value that divides the data into two equal parts.

2. How is a sample mean calculated?

A sample mean is calculated by summing all the values in a data set and dividing it by the total number of values in the set. This gives an average value that represents the central tendency of the data.

3. What does the standard deviation (s.d.) measure?

The standard deviation (s.d.) measures the spread or variability of a set of data. It indicates how much the values deviate from the mean, with a higher standard deviation indicating a larger spread and a lower standard deviation indicating a smaller spread.

4. How does sample size affect the sample mean and median?

A larger sample size tends to result in a more accurate and representative sample mean and median, as it reduces the impact of outliers and random variation. A smaller sample size may lead to a less accurate estimate of the mean and median.

5. Is it necessary to have a large sample size for accurate results?

The necessary sample size for accurate results depends on the type of data and the desired level of precision. In general, a larger sample size is preferred for more reliable results, but it is not always necessary. Statistical techniques can be used to determine the appropriate sample size for a given study or analysis.

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