What is the formula used to calculate kurtosis?

The formula used to calculate kurtosis is correctly represented by the first choice: (xi - xavg)^4 / n*s^4. This formula captures the essence of kurtosis, which measures the "tailedness" of the probability distribution of a real-valued random variable.

Kurtosis is defined as the fourth standardized moment of a distribution, which involves taking each data point, subtracting the mean (xavg), raising the result to the fourth power, and then normalizing by the sample size (n) and the fourth power of the sample standard deviation (s). This normalization ensures that kurtosis is scale-invariant and provides meaningful comparisons across different datasets.

Kurtosis helps in understanding the propensity of a distribution to produce outliers. A higher kurtosis indicates a distribution with more extreme outliers, while a lower kurtosis suggests a more uniform distribution with fewer extreme values.

The other choices provided do not accurately represent the kurtosis calculation. The second choice focuses on the third standardized moment, which corresponds to skewness, indicating the asymmetry of a distribution rather than its tailedness. The third choice refers to the second standardized moment, which measures variance, and the fourth option suggests a fifth power which does not apply to