Are You Being Fooled? The Truth About Liars and Statistics.

A quick and dirty primer on statistical manipulation. You May be surprised.

When we come across statistics in our daily readings, it's always a good idea to pause and examine whether those numbers are presented honestly. We all hope that statisticians, researchers, and journalists will be transparent when using averages in their reports. So, let's explore this concept together! And before we begin, there's a timeless saying about statistics that I think you'll find illuminating:

Three types of lies are ranked by severity: 1. Ordinary lies, 2. Damned lies, and the worst of all, 3. Statistics. This wise saying encourages us to double-check the averages we encounter since not everything is as straightforward as it seems. Sometimes, averages can be misleading, making "caveat emptor" — or "let the buyer beware" — an essential mantra to embrace. This reminds us that not all averages are created equal. It’s a call for you to be discerning and analyze the data critically, especially when it seems too good to be true or is used to back a specific argument or narrative.

So, how do we navigate through these numbers? Let’s start with some basic concepts. The **mean** is what most people consider the average: it’s calculated by summing all the values and then dividing by the total number of entries, known as N. The **mode** represents the number that appears most frequently in a data set, while the **median** is the middle value. If the data set has an even number of values, you simply average the two middle numbers. If you’re curious about deeper statistical concepts or unique scenarios (like when there’s no mode), I recommend exploring them, but for now, we’re focusing on a quick and effective way to spot inconsistencies.

Let’s illustrate this with a fun example involving two fictional island nations. Picture **Alfania** and **Betania**, both with ten residents. Calculating their average incomes is quite straightforward!

Imagine that in **Alfania**, every citizen earns $100,000. When we add up the incomes—$1,000,000 in total—and divide by 10, we find that the average income is indeed $100,000. Easy, right?

Now, let’s compare that to **Betania**. In this case, nine residents earn nothing at all, while the tenth resident rakes in $1,000,000. So again, our total income lands us at $1,000,000, and if we divide that by 10, we arrive at the same average of $100,000. But wait a minute! Can you spot what’s bothering me?

In Alfania, every citizen enjoys a comfortable six-figure salary, while in Betania, the reality is starkly different – nine people live in poverty while one person lives extravagantly. We have not considered their assets or what they own, but focusing purely on income reveals significant disparities.

Even though the means (average incomes) are identical, these two islands present drastically different economic realities. To really understand the situation, we should check the median income. In Alfania, where everyone earns $100,000, the median is straightforward: it’s $100,000 too! For Betania, however, the median falls to $0, reflecting the dire circumstances of the nine less-fortunate residents. The **mode** follows this same pattern—it’s $0 in Betania—as that number appears most frequently among the data set.

So, what does this tell us? When evaluating averages, they should ideally align with the median and mode to reflect a solid measure of central tendency. In the case of **Alfania**, all three measures tell a consistent, optimistic story – everyone is thriving! In stark contrast, Betania’s average income of $100,000 is a glaring outlier when juxtaposed with the median and mode of $0. This discrepancy raises important questions about how accurately we can assess the wealth and well-being of a community based on just one statistic.

What if someone uses these averages to support a narrative or policy? For instance, imagine a political campaign arguing against spending on public services for either island, claiming that both are affluent with an average income of $100,000 per person. While they may have the numbers, we must approach this reasoning cautiously. It’s crucial to delve deeper into the data, recognizing that averages can sometimes mask the true story behind the figures.

You can become a more informed reader and critical thinker by understanding the importance of checking the median and mode alongside the mean. This way, you can sift through the statistics presented to you, spotting potential discrepancies and advocating for a more sincere dialogue about economic policies and social welfare.

So, as you continue your journey through the world of statistics and data, remember to stay curious, vigilant, and enthusiastic! Doing so will help ensure that discussions around data lead to informed decisions that truly benefit everyone. Keep analyzing, questioning, and seeking out the deeper truths behind the numbers. You've got this!

Interesting note: A brilliant Nepali professor, Dr. Shukla of Ohio University, imparted this knowledge to a graduate statistics class in the early 1980s. It has saved me from many, possibly unfortunate blenders. I learned how frequently one encounters statistical liars, even in reputed academic journals. Be aware out there!