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.
No. Skewness is 0, but kurtosis is -3, not 3.No. Skewness is 0, but kurtosis is -3, not 3.No. Skewness is 0, but kurtosis is -3, not 3.No. Skewness is 0, but kurtosis is -3, not 3.
describe the properties of the standard deviation.
skewness=(mean-mode)/standard deviation
When the data are skewed to the right the measure of skewness will be positive.
Answer this question...similarities and differences between normal curve and skewness
distinguish between dispersion and skewness
the use of the pearson's of skewness
if coefficient of skewness is zero then distribution is symmetric or zero skewed.
No. Skewness is 0, but kurtosis is -3, not 3.No. Skewness is 0, but kurtosis is -3, not 3.No. Skewness is 0, but kurtosis is -3, not 3.No. Skewness is 0, but kurtosis is -3, not 3.
skewness=(mean-mode)/standard deviation
describe the properties of the standard deviation.
When the data are skewed to the right the measure of skewness will be positive.
Answer this question...similarities and differences between normal curve and skewness
Skewness is measured as the third standardised moment of the random variable. Skewness is the expected value of {[X - E(X)]/sd(X)}3 where sd(X) = sqrt(Variance of X)
The skewness of a random variable X is the third standardised moment of the distribution. If the mean of the distribution is m and the standard deviation is s, then the skewness, g1 = E[{(X - m)/s}3] where E is the expected value. Skewness is a measure of the degree to which data tend to be on one side of the mean or the other. A skewness of zero indicates symmetry. Positive skewness indicates there are more values that are below the mean but the the ones that are above the mean, although fewer, are substantially bigger. Negative skewness is defined analogously.
Negative skewness means the average (mean) will be less than the median. Positive skewness means the opposite. I'm not sure if any rule holds for the mode.
Skewness is not a characteristic.