Numbers, being numerical, represent amounts: ratios, additions, subtractions, multiplications, divisions. Born of formulas, the products of mathematics, how could numbers ever be untrue or misleading? Numbers affect our lives daily, nonstop, but it's not merely the numbers in and of themselves we must carefully consider but their sources: who or what created, collected, or presented those numbers, and why.
In statistics, when there's a poll (survey), we often hear of a margin of error, which has to do with how representative the statistical claims of a survey might be based on the number of persons polled (questioned) on a particular topic or issue.
Margins of Error
The margin of error relates to the size of the sample - the number of people surveyed: the larger the sample (the more people are polled), the smaller the margin of error is said to be. To put it another way: the smaller the sample (the fewer people are polled), the greater the margin of error. But that's not nearly the extent of how statistics might fail to accurately represent real numbers or situations.Formulas
Formulas (mathematic statements) and equations (mathematical expressions of one set of numbers equaling another) are where many numbers originate. Formulas and equations make use of variables (letters like a, b, c, or x, y, z) which represent numbers (which can come from other equations). How those equations are created (and what variables they include or exclude) will decide the final numerical results.Variables
As more variables are introduced into formulas and equations, mathematical operations and the numbers they generate can become extremely complicated, often to the point that even statisticians, mathematicians, scientists, or economists can have a hard time understanding the results.Calculations, Interpretations
Calculations can be checked - confirmed mathematically, - but then something abstract (non-mathematical) can come into play: interpretation. What might those numbers mean to someone?How someone interprets certain numbers - either when constructing a formula or equation or when looking at the results of a calculation - can change everything, including (if you are unaware) your perception of those numbers and what they are said to represent.
Beyond Numbers
Despite all the apparent impartiality of numbers, the meaning of those numerical results might ultimately come down to personal perspective: how someone sees or wants to portray those numbers. And here we have something else we must consider: agenda.What might someone want us to believe based on those numbers? Could it be that person intends to use those numbers to promote a particular perspective on an issue or a certain cause? How might those intentions influence you or someone else?
Questioning Numbers and Their Sources
There are many questions worth asking!Where polls/surveys are involved...
- Who conducted the poll?
- How were the questions or options phrased? Were they presented in such a way to reach a certain outcome?
- How large was the sample? Were many or few people asked? Does the poll reflect a statistical majority view? Was the margin of error reported? How large or small was that margin?
- Where and when was the poll conducted?
- Was the survey casually conducted or scientific and professionally done?
- Was the poll on the Web and subject to multiple votes per person?
- Are there other polls of a similar nature you can use for comparison?
- Are the original poll/survey questions available for further inspection?
- How would you have responded to the poll?
Statistics
Some questions to consider when you encounter any statistics or numbers...
- Where did the numbers come from? Who or what provided them?
- Are the numbers current (up-to-date) or based on old figures or outdated formulas/equations? What (if any) equations or formulas were used?
- Are any motives involved?
- Might someone (or something) gain or lose something through the way the numbers are presented?
- Are the numbers simply the product of someone's personal interpretation, or are they actually factual?
- Is the presenter of the numbers attempting to correlate (show relationships between) two or more sets of numbers? If any such correlations were used, what was the reasoning involved? Are there real or imaginary (fabricated/madeup) relationships between the sets of numbers?
- Is anything being deliberately obscured, confused, or unaccounted for (omitted) by the numbers?
- Can the numbers be confirmed elsewhere through other sources?
- Were the numbers visually presented? Were charts, graphs, colors, or graphics used? If so, how might such visuals impact the presentation and interpretation of those numbers?
- Are the numbers static (unchanging) or subject to change?
- Is the raw data (i.e. the numbers as they were collected or generated before they were processed/prepared for presentation) available so you can investigate further? How would you interpret the numbers?
- Especially during an election year, with so many numbers loudly touted in dizzying discussions and debates involving things like the economy, "economic indicators," "job growth," and other topics, it is important to realize how numbers can be either misleading or informative in any given situation. Under such circumstances, the neatness and neutrality of numbers can quickly disappear in rhetoric or propaganda.
Stock brokers and analysts monitor financial numbers around the clock while investors base crucial decisions on everchanging amounts. Currencies around the world are subject to constant change. News media outlets often report trends (and in doing so can promote or prolong trends) based on periodic surges or downturns of numbers...
Choices
As these seemingly impersonal numerical phenomena exert incredible influence throughout our lives, we have a simple choice: accept them at face value or begin to ask some questions. This is essential if we want to reach the truth, whether if it involves a product we might want to purchase, a fantastic statistical claim, or any figures affecting our decisions and ideas.Critical thinking skills - asking questions and evaluating information - are absolutely relevant and required wherever there is information of any kind to be examined. Where numbers are involved, having a firm grasp of basic math can help you make better sense of the numbers you encounter, but there are also some fairy easy-to-understand books which can help to raise your awareness of potentially deceptive digits.
The Calculus of Common Sense
Mathematics aside for a moment, sometimes a "truth" will come down to simple logic, common sense, along, perhaps, with an awareness of the limitations of numbers, how they might fail to produce a truly complete account of a situation.After all, in real life so many things escape or defy quantification - being expressed as mere numbers - and there might come the opportunity (or perhaps the need) for you to advance beyond equations, formulas, or any figures presented as so-called facts, toward deeper or more basic inquiries mathematics cannot answer.