Taking care of business, one python script at a time

Tue 26 January 2016

Posted by Chris Moffitt in articles

## Introduction

Pandas includes multiple built in functions such as  sum ,  mean ,  max ,  min , etc. that you can apply to a DataFrame or grouped data. However, building and using your own function is a good way to learn more about how pandas works and can increase your productivity with data wrangling and analysis.

The weighted average is a good example use case because it is easy to understand but useful formula that is not included in pandas. I find that it can be more intuitive than a simple average when looking at certain collections of data. Building a weighted average function in pandas is relatively simple but can be incredibly useful when combined with other pandas functions such as  groupby .

This article will discuss the basics of why you might choose to use a weighted average to look at your data then walk through how to build and use this function in pandas. The basic principles shown in this article will be helpful for building more complex analysis in pandas and should also be helpful in understanding how to work with grouped data in pandas.

## Why Use A Weighted Average?

A simple example shows why the weighted average can be a helpful statistic. The table below shows the prices and quantities that 3 different customers pay for the same product.

Customer Shoe Price Shoe Quantity
Small Customer 300 20
Medium Customer 200 100
Big Customer 150 225

If someone were to ask, what is the average price of our shoes? The simple average of the shoe prices would be:

\begin{equation*} \frac{300+200+150}{3} = \$216.67 \end{equation*} While this is an accurate average, this does not intuitively make sense for understanding our average selling price. This is especially challenging if we want to use an average for revenue projections. If you look at the numbers, you can see we are selling far more shoes for <$200 than we are above $200. Therefore an average of$216.67 does not accurately reflect the real average selling price in the market.

What would be more useful is to weight those prices based on the quantity purchased. Let’s build a weighted average such that the average shoe price will be more representative of all customers’ purchase patterns.

A weighted average can be calculated like this:

\begin{equation*} \frac{(300*20 + 200*100 + 150*225)}{(20 + 100 + 225)} = \$173.19 \end{equation*} Since we are selling the vast majority of our shoes between$200 and \$150, this number represents the overall average price of our products more accurately than the simple average.

This concept is simple but can be a little bit more difficult to calculate in pandas because you need two values: the value to average (shoe price) and the weight (shoe quantity). Let’s walk through how to build and use this in pandas.

## Calculating Weighted Average in Pandas

As shown above, the mathematical concept for a weighted average is straightforward. Because we need values and weights, it can be a little less intuitive to implement in pandas when you are doing complex groupings of data. However, once you figure it out, it can be incredibly easy to use the weighted average in a bunch of different scenarios.

Additionally, the process of building out this functionality and using it in various situations should be useful for building your day to day pandas data manipulation skills. Before I go any further, I wanted to call out that the basic code for this function is based on this Stack Overflow question.

We are going to use a simple DataFrame that contains fictious sales data as the basis for our analysis. Let’s start by importing all the modules we need and read in our Excel file:

import pandas as pd
import numpy as np


Account Name State Rep Manager Current_Price Quantity New_Product_Price
0 714466 Trantow-Barrows MN Craig Booker Debra Henley 500 100 550
1 737550 Fritsch, Russel and Anderson MN Craig Booker Debra Henley 600 90 725
2 146832 Kiehn-Spinka TX Daniel Hilton Debra Henley 225 475 255
3 218895 Kulas Inc TX Daniel Hilton Debra Henley 290 375 300
4 412290 Jerde-Hilpert WI John Smith Debra Henley 375 400 400

In our example data, we have a bunch of account information that includes a current price and quantity as well as a projected New_Product_Price.

If we want to determine a simple mean, we can use the built in functions to easily calculate it:

sales["Current_Price"].mean()
sales["New_Product_Price"].mean()

405.41666
447.08333


In order to calculate a weighted average using the long approach:

(sales["Current_Price"] * sales["Quantity"]).sum() / sales["Quantity"].sum()
(sales["New_Product_Price"] * sales["Quantity"]).sum() / sales["Quantity"].sum()

374.6383
342.5406

Some of the more experienced readers may be wondering why we do not use Numpy’s average function? We absolutely could but I wanted to show how to create a formula. At the end of the article, I will show how to use  np.average

The weighted average formula is not complicated but it is verbose. It also is going to be difficult to use when we group data. Life will be much easier if we build a function for calculating the data.

## Grouping Data with the Weighted Average

Panda’s  groupby is commonly used to summarize data. For instance, if we want to look at the mean of the Current_Price by manager, it is simple with  groupby :

sales.groupby("Manager")["Current_Price"].mean()

Manager
Debra Henley     423.333333
Fred Anderson    387.500000
Name: Current_Price, dtype: float64


Ideally we would like to do the same thing with the weighted average, but how do we pass in the weights we want to use? Hmmm.

The answer is to define a custom function that takes the names of the columns of our data and calculates the weighted average. Then, use  apply to execute it against our grouped data.

def wavg(group, avg_name, weight_name):
""" http://stackoverflow.com/questions/10951341/pandas-dataframe-aggregate-function-using-multiple-columns
In rare instance, we may not have weights, so just return the mean. Customize this if your business case
should return otherwise.
"""
d = group[avg_name]
w = group[weight_name]
try:
return (d * w).sum() / w.sum()
except ZeroDivisionError:
return d.mean()

Handling Division by Zero
In this code, I made the decision that if there is a 0 quantity in the total weight, I want to return the simple mean. In your case you might want to return a  NaN or some other value. This is one example of the power you have by building your own function.

In order to get our weighted average:

wavg(sales, "Current_Price", "Quantity")

342.54068716094031


The nice thing is that this will also work on grouped data. The key is that we need to use  apply in order for pandas to pass the various groupings to the function.

sales.groupby("Manager").apply(wavg, "Current_Price", "Quantity")

Manager
Debra Henley     340.665584
Fred Anderson    344.897959
dtype: float64


Using this on our projected price is easy because you just need to pass in a new column name:

sales.groupby("Manager").apply(wavg, "New_Product_Price", "Quantity")

Manager
Debra Henley     372.646104
Fred Anderson    377.142857
dtype: float64


It is also possible to group by multiple criteria and the function will make sure that the correct data is used in each grouping:

sales.groupby(["Manager", "State"]).apply(wavg, "New_Product_Price", "Quantity")

Manager        State
Debra Henley   MN       632.894737
TX       274.852941
WI       440.000000
Fred Anderson  CA       446.428571
NV       325.000000
WA       610.000000
dtype: float64


This is a simple but really useful approach to understanding your data better.

## Multiple Aggregations

One final item I wanted to cover is the ability to perform multiple aggregations on data. For instance, if we want to get the mean for some columns, median for one and sum for another, we can do this by defining a dictionary with the column names and aggregation functions to call. Then, we call it on the grouped data with  agg

f = {'New_Product_Price': ['mean'],'Current_Price': ['median'], 'Quantity': ['sum', 'mean']}
sales.groupby("Manager").agg(f)

New_Product_Price Current_Price Quantity
mean median sum mean
Manager
Debra Henley 471.666667 437.5 1540 256.666667
Fred Anderson 422.500000 375.0 1225 204.166667
Call for input
If you do know how to do this with a custom (non-lambda) function, please let me know in the comments.

Unfortunately, I could not figure out how to do something similar with a custom function that takes arguments. I’m hoping that I am missing something and that a reader will point it out. In the meantime, here is the approach I use to combine multiple custom functions into a single DataFrame.

First create two datasets of the various weighted averages:

data_1 = sales.groupby("Manager").apply(wavg, "New_Product_Price", "Quantity")
data_2 = sales.groupby("Manager").apply(wavg, "Current_Price", "Quantity")


Then combine them into a single DataFrame and give it a meaningful label:

summary = pd.DataFrame(data=dict(s1=data_1, s2=data_2))
summary.columns = ["New Product Price","Current Product Price"]

New Product Price Current Product Price
Manager
Debra Henley 372.646104 340.665584
Fred Anderson 377.142857 344.897959

I have actually found myself using this pattern in several different scenarios so I’m hoping it is useful to others as well.

## Using Numpy

As I mentioned above, Numpy has an average function which can take a list of weights and calculate a weighted average.

Here is how to use it to get the weighted average for all the ungrouped data:

np.average(sales["Current_Price"], weights=sales["Quantity"])

342.54068716094031


If you want to call this on grouped data, you would need to build a  lambda function:

sales.groupby("Manager").apply(lambda x: np.average(x['New_Product_Price'], weights=x['Quantity']))

Manager
Debra Henley     372.646104
Fred Anderson    377.142857
dtype: float64


## Conclusion

Sometimes when I’m working with pandas, I know something is possible but get stuck on a minor implementation detail that trips me up. The process I describe above shows one example of how I worked through a relatively simple math problem and built a robust solution in pandas that can work on grouped or ungrouped data. The principals shown here can be used to build your own complex formulas for your own needs. If you would prefer looking at this in a notebook, you can find it on github.

Thanks for reading and if you have any input or suggestions, feel free to comment below.