Probability and Statistics - Uh?

Most people have an aversion to math. The root of the problem is that they were taught things like algebra and calculus in school, and then they never used them again. For the most part, basic arithmetic seems to be the only branch of math the average individual ever uses. After all, when was the last time you even had to figure the square root of something? You might also think the odds are pretty low that you'll ever need to use probability and statistics. You'd be wrong about this, though. These branches of math pop up routinely in normal activities. While not understanding them can put you at a severe disadvantage, it's also important to use them consistently wherever they apply.
Just to refresh your memory, probability is essentially all about the likelihood or odds of something happening. Statistics has to do mainly with averages. Put another way, statistics involves looking a large numbers of things and averaging them out. Probability deals with how those averages apply to you. The most basic version of probability that you're probably aware of is the coin flip. A coin has only two sides. When it's flipped, it can only land on one or the other side. This gives you a fifty-fifty probability of one particular side facing up.
With more possibilities, the chances of a particular one happening become smaller. It's impossible to avoid dealing with probability in day-to-day living. When you're choosing between two brands of an item, you'll pick the one that has a smaller percentage of malfunctions. You might be willing to spend the money needed to attend college because it increases the likelihood of getting a high-paying job.
Statistics involves comparing a lot of individual items in order to come up with a typical example. A simple example would be figuring the average age in a group of people. If their ages were ten, fourteen, thirty, and fifty, the average age would be twenty-six. This is obtained by adding the numbers together and dividing by four, the number of individual ages. Statistical averages are used when you decide where to live based on average temperatures or what career to pursue based on average income. It should be kept in mind that the more objects that are used in computing an average, the more accurate it will be. It also needs to be noted that a distorted image can sometimes be created from an average.

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Statisticians use another concept called a median to correct for this. You may want a particular career because its average salary is \$47,500. The problem is that for every person making \$100,000, there are four people making \$30,000. With a median, the incomes would be arranged from lowest to highest and the two middle examples would be averaged. This would provide a median of \$30,000. What this demonstrates is that without this knowledge, it's very easy to be fooled by misleading numbers.  d.