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In mathematical terms, a "mean" is an average. Averages are calculated to represent a data set meaningfully. For instance, a meteorologist could tell you that the mean temperature for January 22 in Chicago is 25 degrees F based on past data. This number cannot predict the exact temperature for next January 22 in Chicago, but it tells you enough to know that you should pack a jacket if you are going to Chicago on that date.
Two commonly used means are the arithmetic mean and the geometric mean. Knowing which one to use for your data means understanding their differences. The most obvious difference between the arithmetic mean and the geometric mean for a data set is how they are calculated. The arithmetic mean is calculated by adding up all the numbers in a data set and dividing the result by the total number of data points.
The geometric mean of a data set is calculated by multiplying the numbers in the data set, and taking the nth root of the result, where "n" is the total number of data points in the set. When you look at the results of arithmetic mean and geometric mean calculations, you notice that the effect of outliers is greatly dampened in the geometric mean.
What does this mean? In the data set of 11, 13, 17 and 1,, the number 1, is called an "outlier" because its value is much higher than all the other ones. When the arithmetic mean is calculated, the result is Notice that no number in the data set is even close to The outlier's effect has been exaggerated.
The geometric mean, at Statisticians use arithmetic means to represent data with no significant outliers. This type of mean is good for representing average temperatures, because all the temperatures for January 22 in Chicago will be between and 50 degrees F. A temperature of 10, degrees F is just not going to happen.
Things like batting averages and average race car speeds are also represented well using arithmetic means. Geometric means are used in cases where the differences among data points are logarithmic or vary by multiples of Biologists use geometric means to describe the sizes of bacterial populations, which can be 20 organisms one day and 20, the next.
Economists can use geometric means to describe income distributions. The arithmetic mean of the income in your neighborhood would be misleading here, so a geometric mean would be more suitable.
Timothy Banas has a master's degree in biophysics and was a high school science teacher in Chicago for seven years. He has since been working as a trading systems analyst, standardized test item developer, and freelance writer.
As a freelancer, he has written articles on everything from personal finances to computer technology. About the Author. Photo Credits. Copyright Leaf Group Ltd.
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Mathematics for Self Study Arithmetic for the practical man, , 25th printing. This is a 1st edition but the 25th printing which was in (thus the wartime paper edict). The book is in G/Fair shape, bottom corners are bent with slight scuff marks, spine is bumped with slight scuffing also. Binding is tight. 3 small spots of foxing on pages but nowhere else in book that I one.calcionotizie24.net Rating: % positive. May 11, · In the s it would have been unusual for a high school to have a calculus instructor, and trigonometry was the highest level of math taught at Feynman’s Far Rockaway High School in New York. Math professor James Edgar Thompson’s Practical Man series of self-instruction books seemed like just the way to learn more. Refresher Arithmetic With Practical Applications Vintage high school math text in vintage used condition (bumped corners, wear to the cloth spine at the top and bottom). Tight spine and no loose pages. Ex-school marking and original owners name at front of book. I didnt find any marks within.