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Does the empirical rule work for any data set?
No.The empirical rule is a good estimate of the spread of the data given the mean and standard deviation of a data set that follows the normal distribution.If you you have a data set with 10 values, perhaps all 10 the same, you clearly cannot use the empirical rule.
What does one standard deviation mean?
Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.
What is the difference between Chebyshevs inequality and empirical rule in terms of skewness?
Chebyshev's inequality: The fraction of any data set lying within K standard deviations is always at least 1-1/K^2 where K is any positive number greater than 1. It does not assume that any distribution. Now, there is the empirical rule of bell shaped curves or the 68-95-99.7 rule, which states that for a bell shaped curve: 68% of all values should fall within 1 standard deviation, 95% of all values should fall within 2 standard deviations and 99.7% of all values should fall within 3 standard deviation. If we suspect that our data is not bell shaped, but right or left skewed, the above rule can not be applied. I note that one test of skewness is Pearson's index of skewness, I= 3(mean of data - median of data)/(std deviation) If I is greater or equal to 1000 or I is less than 1, the data can be considered significantly skewed. I hope this answers your question. I used the textbook Elementary Statistics by Triola for the information on Pearson's index. If this answer is insufficient, please resubmit and be a bit more definitive on what you mean by empirical rule.
In research how to define standard deviation?
Standard deviation shows how much variation there is from the "average" (mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
What is the relationship between standard deviation and variance for the same sample data?
The standard deviation is the square root of the variance.
