skewness and kurtosis are aggregate functions that describe the shape of a numeric distribution rather than its center or spread. Skewness measures how asymmetric the values are, and kurtosis measures how heavy the tails are. Both are handy for spotting outliers and non-normal data before you rely on averages or standard deviations.

Standard deviation and variance measure how spread out the values in a numeric column are. Spark provides a full family of aggregate functions for both — stddev, stddev_samp, and stddev_pop for standard deviation, and variance, var_samp, and var_pop for variance. The only real decision you have to make is whether you want the sample or population form.

collect_list and collect_set are aggregate functions that gather the values in each group into an array. collect_list keeps every value, including duplicates; collect_set keeps only the distinct ones. array_agg is a SQL alias for collect_list. They're the go-to tools when you want to roll many rows up into a single row that holds all their values.

first and last are aggregate functions that return the earliest or latest value in a group — but only when the data is ordered. They're most useful as window functions paired with an orderBy clause, where "first" and "last" actually mean something specific. first_value and last_value are SQL-only synonyms, and any_value returns an arbitrary value when you don't care which one you get.

min and max are aggregate functions that return the smallest and largest values in a column. min_by and max_by go a step further — they return the value of one column at the row where another column reaches its extreme, so you can answer questions like "which employee earns the highest salary?" rather than just "what is the highest salary?".

avg and mean are aggregate functions that compute the arithmetic mean of values in a numeric column. They're the workhorse functions for summarizing data — average salary by department, average order size by region, moving average of a stock price. The two functions are identical; mean is just an alias for avg.

sum is an aggregate function that totals the values in a numeric column. It's one of the most common operations in Spark Scala — used to roll up sales totals, computed metrics, running balances, and just about any group-level numeric summary.

count, countDistinct, and count_if are aggregate functions for counting rows in a Spark Scala DataFrame. count counts rows or non-null values, countDistinct counts unique values, and count_if counts rows that match a condition.

The bitwise shift functions move the bits of an integer column left or right by a fixed number of positions. They're useful for packing and unpacking flags, fast multiplication or division by powers of two, and working with binary protocol data.

e() returns Euler's number (≈ 2.71828) and pi() returns π (≈ 3.14159). They're handy when a Spark expression needs one of these mathematical constants — for circle math, exponential growth, trigonometry, and so on — without you having to hard-code the literal value.