Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Univariate Data Measures of Location Mean Mean  
See also: Median, mode, Standard Deviation, Comparing means, Central Limit Theorem, confidence interval, Generalized Mean  
MeanThe mean is commonly called the average. From a mathematical standpoint there are several types of means which are legitimate in various scenarios:
Here is a simple interactive example for a "natural" computation of the mean. Please note that there are different notations for the mean: the mean of a population is denoted by μ, whereas the mean of the scores of a sample is denoted either by m, or by . The mean is a good approximation of the central tendency for unimodal symmetric distributions, but can be misleading in skewed or multimodal distributions. Therefore, it can be useful to specify other additional measures of location for skewed distributions (i.e. the median is more robust in case of skewed distributions or or in case of outliers). Another way to deal with outliers is to use a trimmed mean, which is calculated after the lower and upper fraction (typically 5%) of the values have been discarded. Hint 1: It can be shown that the sum of squared deviations of sample scores from their mean is lower than the squared deviations from any other value. Hint 2: The mean is also often related to the accuracy of an experiment. See the following interactive example to get an impression of accuracy versus precision.


Home Univariate Data Measures of Location Mean Mean 