It seems that with increasing frequency, statistics are appearing in the news media and in the advertising of companies trying to sell you a product. With all the polls and data being reported, how can you be certain that you’re being given an accurate representation of the facts? Are you ever concerned that you’re really getting the whole picture when someone presents you with percentages? With a good understanding of a few basic statistical terms, you can be well on your way to understanding what all the data is truly telling you.
Mean: This is one of the most commonly used statistical terms that you’ll see utilized. To calculate the mean, you simply add together all of the values in your data set, and divide that sum by the total number of values in the set of data.
Example: Seven students took a standardized test. One student scored 100, three students scored 75, and three students scored 25. The mean score would be 400 divided by 7, or 57.
Median: Often confused with the mean, the median is actually something different altogether. The median is actually the value that is the middle value of the data set. To establish the median, line up the data in ascending order, and find the data point that’s right in the middle.
Example: Let’s look once again at the above set of standardized test scores. In ascending order, the scores are as follows…
25, 25, 25, 75, 75, 75, 100
Halfway across the list, the fourth and median value of this data is 75. But think about this…if you were a company that offered preparation courses for standardized test, and this data set represented the scores that your most recent class achieved, you could make your business look more attractive by advertising a median score of 75, as opposed to a mean score of 57. Asking the correct questions and knowing the real data could help you make a more informed purchase decision.
Mode: This term is used less frequently, but it’s a good one to know, just in case. The mode is simply the value that occurs most frequently in a set of data.
Example: Let’s assume that five additional test scores were obtained to supplement the scores from the previous example. They are 100, 95, 90, 80 and 25. Even though these scores would raise both the mean and the median, these would cause the mode to be 25.
Average: This is one to be careful with. When most people use the word average, they usually use it as a synonym for mean, which is sometimes called the arithmetic average. However, statistically, the words mean, median and mode are just a few of the terms that someone could intend when using the word average. If you’re uncertain of precisely what someone means when they call a number the average, don’t be afraid to ask how they arrived at that number.
Range: This is simply the difference between the largest value in a set of data and the smallest value in that same data set.
Example: Using the set of fifteen test scores described above, the range would be 100-25, or 75.
Margin of Error: This term appears frequently on news programs, particularly when the results of a poll are described. Understanding margin of error is key to understanding what poll data is really saying. Margin of error is a way of describing approximately how many percentage points a poll may be off by.
Example: Let’s say that a very controversial proposition is coming up for a vote in your area. On your local news station, the news teams reports that a recent poll revealed that 54% of the voting population was in favor of the proposition, and 46% of the population was opposed to the proposition. As a footnote, the margin of error is listed as +/-5%. What this means is that the number of people polled was large enough to assert that it is 95% certain that the true opinion of the population would be within 5% of the data reported. Therefore, it’s possible that anywhere between 49% and 59% of the voters are in favor of passing the proposition. So, even though it seems at first like voters are supportive of the proposition, in reality, the statistics indicate that those who oppose the proposition may be of the majority.
Random Sample: This phrase is a bit more difficult to pin down. However, it’s important to be certain that the participants in a poll are randomly selected, or the results may be skewed.
Example: Local hamburger stand A claims that 95% of people polled think that stand A’s fries are better tasting than the fries sold at hamburger stand B. However, if this data were compiled by asking customers at stand A to fill out a survey, it would not be appropriate to call this sampling random. After all, there’s a strong chance that customers at stand A may prefer the fries from the stand that they’ve chosen to patronize.
When in doubt, it’s always best to question the data that you’re presented with. A school boasts of a 92% graduation rate, but how did the school perform in previous years? If the prior few years had graduation rates of 95% and above, then the 92% may represent a negative trend. However, compared to other schools in the area, 92% may still be a number to be proud of.
Don’t let statistics intimidate you! It’s not difficult to understand what the data means if you understand the language of statistics.
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