Yes. If much of your data has negative values, it's likely that the mean will be negative, too.
negative means someone saying No
z-score of a value=(that value minus the mean)/(standard deviation). So if a value has a negative z-score, then it is below the mean.
It depends on the context. It may mean quiet, unruffled (positive) or it could mean too laid back to do anything (negative).
It can be negative, zero or positive.
The Greek word "kurtosis", when translated to English, means the probability theory of any measure of the "peakedness" of a real valued random variable.
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.
The mean, variance, skewness, kurtosis and all higher moments of a distribution.
While skewness is the measure of symmetry, or if one would like to be more precise, the lack of symmetry, kurtosis is a measure of data that is either peaked or flat relative to a normal distribution of a data set. * Skewness: A distribution is symmetric if both the left and right sides are the same relative to the center point. * Kurtosis: A data set that tends to have a distant peak near the mean value, have heavy tails, or decline rapidly is a measure of high kurtosis. Data sets with low Kurtosis would obviously be opposite with a flat mean at the top, and a distribution that is uniform.
I will answer your question in a couple of ways. First as a concept: Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case. Now as a mathematical formula: For univariate data Y1, Y2, ..., YN, the formula for kurtosis is:where is the mean, is the standard deviation, and N is the number of data points. You may find more information at this website: http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
mesokurtic leptokurtic platykurtic
In probability theory and statistics, kurtosis (from the Greek word κυρτός, kyrtos or kurtos, meaning bulging) is a measure of the "peakedness" of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestly sized deviations. Sometimes kurtosis gets confused with skewness, so I have added links to both these terms.
For N(0, 1) it is 3.
It is inversely proportional; a larger standard deviation produces a small kurtosis (smaller peak, more spread out data) and a smaller standard deviation produces a larger kurtosis (larger peak, data more centrally located).
The kurtosis of a distribution is defined as the fourth central moment divided by the square of the second central moment. Unfortunately, this browser converts Greek characters to the Roman alphabet so I cannot use standard forms of equations but: Suppose that for a random variable X, E(X) = m (mu) and E[(X - E(X))2] = V = s2 (sigma-squared) then Kurtosis = E[(X - E(X))4]/s4. Excess Kurtosis is then Kurtosis - 3. If excess kurtosis < 0 the distribution is platykurtic. They have a peak that is lower than the Normal: the peak is flat and broad. The tails of the distribution are narrow. Uniform distributions are platykurtic. A mesokurtic distibution has excess kurtosis = 0. The Gaussian (Normal) distribution - whatever its parameters - is mesokurtic. The binomial with probability of success close to 1/2 is also considered to be mesokurtic. If excess kurtosis is > 0 the distribution is leptokurtic. Leptokurtic distributions have a high and narrow peak. A good example is the Student's t distribution.