Standardization is a common statistical procedure to understand how greatly individual values vary from the mean. For a normal distribution, 99.7% of the data lies within three standard deviations of the mean.
A closure is a function that contains a function inside of it (a nested function) and returns this nested function. This nested function must refer to variables in the scope of the outer function in order to be a closure. In this example, `make_agg_func` is the outer function and returns the nested function `wrapper`, which accesses the variables `func`, `args`, and `kwargs` from the outer function.
The `pivot` method only works if there is just a single occurrence of each unique combination of the columns in the `index` and `columns` parameters. If there is more than one unique combination, an exception will be raised. You can use the `pivot_table` method in that situation which allows you to aggregate multiple values together.
To become a powerful user of the `str` methods, you will need to be familiar with regular expressions, which are a sequence of characters that match a particular pattern within some text. They consist of **metacharacters**, which have a special meaning, and **literal** characters. To make yourself useful with regular expressions check this short tutorial from *Regular-Expressions.info* ([http://bit.ly/2wiWPbz](http://bit.ly/2wiWPbz)).
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The result from step 3 isn't quite an exact replication of step 1\. There are entire rows of missing values, and by default, the `stack` method drops these during step 2\. To keep these missing values and create an exact replication, use `dropna=False` in the `stack` method.
In this context, we are using the precise mathematical definition of the transposing of a matrix, where the new rows are the old columns of the original data matrix.
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