Skewness is a measure of the degree of asymmetry of the distribution. The three most important descriptions of shape are Symmetric, Left-skewed, and Right-skewed. The shape of the data helps us to determine the most appropriate measure of central tendency.
logarithmic transformation. We just need to remember the original data was transformed!! When the data is not normal, statisticians will transform the data using numerous techniques e.g. For many applied statistical methods, a required assumption is that the data is normal, or very near bell-shaped. Regression, ANOVA), is the transforming data. Why would you want to know this? One reason, especially for those moving onward to more applied statistics (e.g. As we will learn shortly, the effect is not the same on the variance! Returning to the 10 aptitude scores, if all of the original scores were doubled, the then the new mean and new median would be double the original mean and median. Similarly, if each observed data value was multiplied by a constant, the new mean and median would change by a factor of this constant.
#Metadatics 1.5.1 plus#
What effect does this have on the mean and the median? The result of adding a constant to each value has the intended effect of altering the mean and median by the constant.įor example, if in the above example where we have 10 aptitude scores, if 5 was added to each score the mean of this new data set would be 87.1 (the original mean of 82.1 plus 5) and the new median would be 86 (the original median of 81 plus 5). What happens to the mean and median if we add or multiply each observation in a data set by a constant?Ĭonsider for example if an instructor curves an exam by adding five points to each student’s score. We will discuss methods using the median in Lesson 11. For example, use the sample median to estimate the population median. Unless data points are known mistakes, one should not remove them from the data set! One should keep the extreme points and use more resistant measures. However, we need to be aware of one of its shortcomings, which is that it is easily affected by extreme values. In future lessons, we talk about mainly about the mean. The mean is a sensitive measure (or sensitive statistic) and the median is a resistant measure (or resistant statistic).Īfter reading this lesson you should know that there are quite a few options when one wants to describe central tendency. Therefore the median is not that affected by the extreme value 9. The medians of the two sets are not that different. The data set (with 91 coded as 9) in increasing order is: Let us see the effect of the mistake on the median value. The mean would be 73.9, which is very different from 82.1.
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