Data-driven decision-making is essential for success in product management. And one of the important parts of any kind of data-driven work is measuring and understanding central tendencies in data samples. 

Central tendencies refer to the typical or average values of a set of data points, and they can provide insights into the overall performance of your product. Measuring central tendencies is becoming increasingly important in any kind of decision-making that involves data. And product managers have to make decisions based on data on a daily basis.

There are several ways to measure central tendencies, but the most commonly used methods are arithmetic mean and median. In this article, we will explore these two measures, compare them, and see how they can be used in product work.

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Arithmetic mean

Arithmetic mean is a widely used measure of central tendency in data analysis. It is calculated by adding up all the values in a dataset and then dividing the sum by the total number of values. The formula for arithmetic mean is as follows:

Arithmetic Mean = (Sum of all values) / (Total number of values)

For example, let’s say you are a product manager for an e-commerce website and you want to calculate the average shopping basket value of the previous day. You would first collect data on all the purchases during that time frame. Here is an example:

Arithmetic Mean = ($45 + $32 + $56 + $78 + $23) / 5 = $46.80

Strengths of arithmetic mean in product management

  • The formula for the arithmetic mean is easy to understand and calculate, making it accessible and useful for communicating data insights to stakeholders, such as executives or development teams, who may not have a strong statistical background. 
  • The arithmetic mean takes all values in the dataset into account. 
  • The arithmetic mean is a familiar and intuitive metric that is widely used in many fields. It allows for easy comparison between different datasets and can provide a quick snapshot of overall performance. 

Weaknesses of arithmetic mean in product management

  • The arithmetic mean is highly sensitive to outliers, data points that are significantly different from the rest of the dataset, either much larger or much smaller. Outliers can skew the mean upward or downward, giving an inaccurate representation of the data’s central tendency. In product management, this can lead to misguided decisions or missed opportunities.

    For example, let’s say a product manager is analyzing the average time users spend on their e-learning platform. Most users spend around 30 minutes on the platform, but there are a few outliers who spend over five hours. If the product manager were to solely rely on the arithmetic mean, they would get a much higher value than the typical user’s experience.
  • Arithmetic mean can be expensive to compute for very large datasets. Adding up all the values in a dataset can be time-consuming, and for datasets with millions of data points, it may not be feasible to calculate the mean by hand.

Use cases for arithmetic mean in product management

In product management, the arithmetic mean is a useful tool to use when you want a simple, intuitive metric that represents the overall average or typical value across a set of numbers that don’t have too many outliers. 

One example of when to use the arithmetic mean in product management is when calculating customer satisfaction scores. By using the mean, you can give equal weight to all scores, providing an overall average satisfaction rating that can be used to track changes in customer perception over time.

Another example is when calculating the cost per install for a mobile app. By calculating the mean cost per conversion, you can get a quick snapshot of the app’s overall cost-effectiveness across many conversions. This can be useful in identifying areas for improvement, optimizing ad spend, and enhancing the overall user acquisition strategy.