STATISTICS TERMS

[VLSroulette]

This thread is intended to be a compilation of terms from statistics we must know.

Let's start!



Standard Deviation

Formulated by Galton in the late 1860s, the standard deviation remains the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large. If all data values are equal, then the standard deviation is zero. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.



Dispersion

In statistics, (statistical) dispersion (also called statistical variability or variation) is variability or spread in a variable or a probability distribution.

A measure of statistical dispersion is a real number that is zero if all the data are identical, and increases as the data becomes more diverse. It cannot be less than zero.

Most measures of dispersion have the same scale as the quantity being measured. In other words, if the measurements have units, such as metres or seconds, the measure of dispersion has the same units.



Variance

In probability theory and statistics, the variance of a random variable, probability distribution, or sample is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value (mean). Whereas the mean is a way to describe the location of a distribution, the variance is a way to capture its scale or degree of being spread out. The unit of variance is the square of the unit of the original variable. The positive square root of the variance, called the standard deviation, has the same units as the original variable and can be easier to interpret for this reason.

The variance of a real-valued random variable is its second central moment, and it also happens to be its second cumulant. Just as some distributions do not have a mean, some do not have a variance. The mean exists whenever the variance exists, but not vice versa.



Mean

In statistics, mean has two related meanings:

    * the arithmetic mean (and is distinguished from the geometric mean or harmonic mean).
    * the expected value of a random variable, which is also called the population mean.



Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

The "range" is just the difference between the largest and smallest values.

    * Find the mean, median, mode, and range for the following list of values:

            13, 18, 13, 14, 13, 16, 14, 21, 13

      The mean is the usual average, so:

            (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

      Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

      The median is the middle value, so I'll have to rewrite the list in order:

            13, 13, 13, 13, 14, 14, 16, 18, 21

      There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

            13, 13, 13, 13, 14, 14, 16, 18, 21

      So the median is 14.   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

      The mode is the number that is repeated more often than any other, so 13 is the mode.

      The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

            mean: 15
            median: 14
            mode: 13
            range: 8

Note: The formula for the place to find the median is "( [the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

[VLSroulette]

New submissions are welcome, please add them as a reply below and I'll add them as an edit above.

[VLSroulette]

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