Skewness and kurtosis are important ideas in statistics, especially when we want to understand how data is shaped.

1. Skewness is about how lopsided a distribution is. If a distribution is perfectly normal, it has a skewness of $0$.

   • Positive skewness means that the data has a long tail on the right side.
   • Negative skewness means there’s a long tail on the left side.

   When the data is not symmetrical, it can cause problems with our assumptions, leading to mistakes when we try to make conclusions from the data.

2. Kurtosis looks at how heavy the tails of a distribution are. A normal distribution has a kurtosis of $3$, which means it has what we call an "excess kurtosis" of $0$.

   • If a distribution has high kurtosis, it could mean there are outliers—those extreme values that stand out from the rest of the data.

   • This can make interpreting the data and measuring how well our model works more difficult.

To deal with these challenges, researchers can use techniques to transform the data.

For instance, they might use logarithmic or square root transformations to fix skewness and adjust kurtosis.

Normalization methods like the Box-Cox transformation can also help make the data more normal.

However, these methods aren’t always simple and need to be thought through based on the data we have.