Skill 1.7 Applying mathematics to investigations in chemistry and the analysis of data

Skill 1.7 Applying mathematics to investigations in chemistry and the analysis of data 

To more easily manage large amounts of data, statistical measures are employed to characterize trends in the data. In many systems, the data fits a normal distribution, which has a concentration of data points in the center and two equally sized tails (the ends of the distributions). This type of distribution looks like this  

A distribution is considered skewed if one tail is larger than the other. To further characterize these distributions, a variety of statistical measures are used. The following are the most commonly used statistical measures  

Arithmetic Mean The arithmetic mean is the same as the arithmetic mean or average of a distribution - the sum of all the data points divided by the number of data points. The arithmetic mean is a good measure of the central tendency of roughly normal distributions, but may be misleading in skewed distributions. In cases of skewed distributions, other statistics such as the median or geometric mean may be more informative. 

Median The median is the middle of a distribution half the scores are above the median and half are below it. Unlike the mean, the median is not highly sensitive to extreme data points. This makes the median a better measure than the mean for finding the central tendency of highly skewed distributions. The median is determined by organizing the data points from lowest to highest. When there is an odd number of numbers, the median is simply the middle number. For example, the median of 2, 4, and 7 is 4. When there is an even number of numbers, the median is the mean of the two middle numbers. Thus, the median of the numbers 2, 4, 7, 12 is (4+7)/2 = 5.5. 

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