Median, and the Mode. The Essay

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A standard deviation is so "standardized" that, generally speaking, 70% of the data points will fall within one standard deviation, and 90% of the data points will fall within two standard deviations. Standard deviation is one of the most common ways for researchers to describe data as it forms a basis for comparing data from study to study.

Measures of central tendency are most effective at describing data that shows a more typical normal curve distribution -- in other words, if a data set is characterized by long tails or data points that are considered to be outliers because they are very extreme compared to the rest of the data points in the distribution, the mean will be substantively different than if the data set showed a normal distribution with moderate tails. In such cases, the median can be used to describe the data because it is not affected in the same manner by extreme scores.

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The reason the mean is impacted by extreme scores is because it is calculated by using a sum total of all the data points and then divided by the number of data points. The sum total can be inordinately increased by even one outlier data point, which in turn will skew the average (or mean) which is calculated from this higher (or lower, as the case may be) number.

I particularly like how Tufte stresses that large data sets must be made to be understandable and that data must tell the truth. As Tufte explains, very often, it seems like researchers are focused on making an impression on their readers and do not take steps to make the research findings comprehensible. Obfuscation is not a useful approach to science, even.....

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