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iVenky

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In summary, the conversation discussed finding the confidence interval for standard deviation using the chi-square distribution. The sample size is N=500 and the sample standard deviation is 3 with a mean of 0. The degrees of freedom for this calculation is the sample size minus one (499). There is an online tool available for calculating confidence intervals, but it only provides the interval for the mean, not the standard deviation. Another website provides a specific example and reports the confidence interval for SD as 0.94*SD to 1.07*SD with a sample size of 500 and degrees of freedom of 499.

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iVenky

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.Scott

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Confidence Interval

The degrees of freedom is you sample size minus one (499), but that is not required by this tool.

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iVenky

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Thanks for the reply, but I am interested in confidence interval of the standard deviation rather than the mean. The link that you mentioned doesn't contain the confidence interval for standard deviation

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.Scott

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That tools reports: 2.82 to 3.20

The site below provides a more specific example in one of its tables:

https://www.graphpad.com/guides/prism/7/statistics/stat_confidence_interval_of_a_stand.htm

For the 95% Confidence Interval of the SD and n=500, it reports: 0.94*SD to 1.07*SD

And the degrees of freedom is still 499.

- #5

iVenky

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Thank you very much!

A confidence interval on standard deviation is a range of values that is likely to contain the true population standard deviation with a certain degree of confidence. It is used to estimate the precision of a sample standard deviation and to determine the variability of a population.

A confidence interval on standard deviation is calculated using the sample standard deviation, sample size, and a critical value from the t-distribution. The formula for calculating the confidence interval is: sample standard deviation ± (critical value * standard error of the sample standard deviation).

The purpose of a confidence interval on standard deviation is to provide a range of values that is likely to contain the true population standard deviation. It is used to estimate the precision of a sample standard deviation and to determine the variability of a population.

The confidence level for a confidence interval on standard deviation is typically chosen to be 95%, 99%, or 99.9%. This represents the degree of confidence that the true population standard deviation falls within the calculated interval. A higher confidence level indicates a narrower interval, while a lower confidence level indicates a wider interval.

The assumptions for calculating a confidence interval on standard deviation are that the data is normally distributed and that the sample is representative of the population. If these assumptions are not met, then the confidence interval may not accurately reflect the true population standard deviation.

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