What does it indicate if skewness equals zero and excess kurtosis equals zero in data analysis?

When skewness equals zero and excess kurtosis equals zero, it signifies that the data follows a normal distribution.

Skewness measures the asymmetry of the data distribution. A skewness of zero suggests that the distribution is perfectly symmetric, indicating that the left and right tails of the distribution are equal in length and shape. This is a key characteristic of a normal distribution.

Excess kurtosis assesses the "tailedness" of the probability distribution of a real-valued random variable. A value of zero indicates that the distribution’s tails have the same weight as those of a normal distribution, which has a kurtosis of three. This means that the data does not have heavy tails (or outliers) or light tails, which is also consistent with a normal distribution.

Thus, having both skewness and excess kurtosis equal to zero strongly confirms that the data is normally distributed, distinguishing it from characteristics represented by other options such as heteroskedasticity, high variance, or positive skewness, which introduce different behaviors and shapes in data distribution.