Free Statistics for Dummies by Deborah Jean Rumsey

tells you nothing about the range of house prices you may encounter when house-hunting. The average salary may not fully represent what's really going on in your company, if the salaries are extremely spread out.
REMEMBER 
Don't be satisfied with finding out only the average — be sure to ask for the standard deviation, as well. Without a standard deviation, you have no way of knowing how spread out the values may be. (If you're talking starting salaries, for example, this could be very important!)
    Percentile
    You've probably heard references to percentiles before. If you've taken any kind of standardized test, you know that when your score was reported, it was presented to you with a measure of where you stood, compared to the other people who took the test. This comparison measure was most likely reported to you in terms of a percentile. The percentile reported for a given score is the percentage of values in the data set that fall below that certain score. For example, if your score was reported to be at the 90th percentile, that means that 90% of the other people who took the test with you scored lower than you did (and 10% scored higher than you did). For more specifics on percentiles, see Chapter 5 .
REMEMBER 
Percentiles are used in a variety of ways for comparison purposes and to determine relative standing (that is, how an individual data value compares to the rest of the group). Babies' weights are often reported in terms of percentiles, for example. Percentiles are also used by companies to get a handle on where they stand compared to other companies in terms of sales, profits, customer satisfaction, and so on.
    Standard score
    The standard score is a slick way to put results in perspective without having to provide a lot of details — something that the media loves. The standard score represents the number of standard deviations above or below the mean (without caring what that standard deviation or mean actually are).
    As an example, suppose Bob took his statewide 10th-grade test recently, and scored 400. What does that mean? It may not mean much to you because you can't put that 400 into perspective. But knowing that Bob's standard score on the test is +2 tells you everything. It tells you that Bob's score is 2 standard deviations above the mean. (Bravo, Bob!) Now suppose Bill's standard score is − 2. In this case, this is not good (for Bill), because it means Bill's score is 2 standard deviations below the mean.
    The formula for standard score is
    where
x is the average of all the scores
s is the standard deviation of all the scores
    For the details on calculating and interpreting standard scores, see Chapter 8 .
    Normal distribution (or bell-shaped curve)
    When numerical data are organized, they're often ordered from smallest to largest, broken into reasonably sized groups, then put into graphs and charts to examine the shape, or distribution, of the data. The most common type of data distribution is called the bell-shaped curve , in which most of the data are centered around the average in a big lump, and as you move farther out on either side of the mean, you find fewer and fewer data points. Figure 3-1 shows a picture of a bell-shaped curve; notice that the shape of the curve resembles the outline of an old-fashioned bell.
    Figure 3-1: Bell-shaped curve.
    Statisticians have another name for the bell-shaped curve when many possible values for the data exist; they call it the normal distribution. This distribution is used to describe data that follow a bell-shaped pattern, including what the range of values is expected to be and where an individual score stands in relation to the others. For example, if the data have a normal distribution, you can expect most of the data to lie within two standard deviations of the mean. Because every distinct population of data has a different mean and standard deviation, an infinite number of different normal distributions exist, each with its own mean and its own