median [CapiPedia]

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====== Median ======
The median is the number that sits right in the middle of a set of data when that data is arranged in order from smallest to largest. Imagine lining up a group of people by height; the median height is the height of the person standing in the exact middle. Unlike its more famous cousin, the [[mean]] (or average), the median isn't swayed by extreme values, known as [[outlier|outliers]]. This resilience makes it an incredibly powerful and honest tool for investors. If you have five companies with profits of $1 million, $2 million, $3 million, $4 million, and $100 million, the average profit is a whopping $22 million. This figure is heavily distorted by the one superstar company. The median, however, is simply the middle value: a much more representative $3 million. It gives you a truer sense of what a "typical" company in that group looks like, which is a cornerstone of sound investment analysis.
===== Why the Median Matters in Investing =====
For a [[value investing|value investor]], reality is everything. We want to understand a business or a market for what it truly is, not what a few exceptions make it seem to be. The median helps us cut through the noise and find that reality. Averages can be deceptive, painting a picture that is rosier—or sometimes gloomier—than the truth. The median acts as a reliable anchor, providing a more stable and realistic viewpoint.
==== Median vs. Mean: The Skew Showdown ====
The biggest selling point of the median is its performance in a [[skewed distribution]]—that is, a dataset where a few extremely high or low numbers pull the average in their direction.
Let's see this with a simple example. Imagine you're analyzing the salaries at a small company to gauge its compensation structure. There are 5 employees:
  * Employee A: $50,000
  * Employee B: $55,000
  * Employee C: $60,000
  * Employee D: $65,000
  * CEO: $1,000,000
The **mean** (average) salary is ($50,000 + $55,000 + $60,000 + $65,000 + $1,000,000) / 5 = $246,000. If you were told the "average" salary is $246,000, you'd think it's a very high-paying company for everyone.
Now, let's find the **median**. First, we sort the numbers (they already are). The middle value is $60,000. This figure gives you a //much// more accurate idea of what a typical employee earns. The CEO's massive salary is an outlier that wildly skews the mean but has no effect on the median.
//Pro tip:// If the median and mean of a dataset are far apart, it's a huge red flag telling you to investigate for outliers that might be distorting the bigger picture.
==== Practical Applications for the Value Investor ====
Understanding the median isn't just a fun math trick; it has direct, money-making applications.
=== Analyzing Financial Ratios ===
When you're comparing a company to its peers, using the industry's //median// financial ratios is often more insightful than using the average.
  * **[[P/E ratio]]:** Imagine an industry where most companies trade at a [[Price-to-Earnings Ratio|P/E ratio]] between 10 and 15. However, one speculative, high-growth darling trades at a P/E of 200. This single company could pull the industry //average// P/E up to 30 or 40, making reasonably priced companies look cheap and the expensive ones look normal. The //median// P/E, however, would remain firmly in that 10-15 range, giving you a far better benchmark for what is "normal" and helping you spot genuine bargains.
  * **[[Debt-to-Equity Ratio]]:** Similarly, a few highly leveraged companies can inflate the average debt level for a sector. The median [[debt-to-equity ratio]] tells you what the typical company's balance sheet looks like, helping you assess if your potential investment is carrying a prudent amount of debt.
=== Understanding Economic Data ===
When you read about the economy, pay close attention to whether journalists and analysts are using mean or median figures.
  * **Household Income:** You will often see reports on "median household income." This is the gold standard for understanding the economic well-being of the middle class. The average income is always higher because it is pulled up by billionaires and multimillionaires. The median tells you what the family in the very middle is earning, which is a much better indicator of the purchasing power and financial health of the general population—the very people who buy the products and services of the companies you invest in.
  * **Real Estate Prices:** When assessing a housing market, always look for the //median// home price, not the average. A few mega-mansions can easily inflate the average price of a neighborhood, making it seem unaffordable. The median price gives you a more realistic idea of what a typical home in that area costs.