![]() This is a very rough indicator, though, as it is extremely sensitive to outliers. Knowing the location of a variable is not enough for our purpose as we miss an important information: how close are the values to the mean? The simplest statistic to express the spread is the range, that is the difference between the highest and lowest value. Considering that extreme values (very high or very low) are usually known as outliers, we say that the median is more robust than the mean with respect to outliers. For example if we take the same values as above (1 - 4 - 7 - 9 - 10), the median is equal to 7 and it is not affected when we change the highest value into 100. The median is always the central value in terms of positioning, i.e., the number of values above the median is always equal to the number of values below the median. Otherwise, if the number of values is even, we take the two values in the \(n/2\) and \(n/2 1\) positions and average them. If the number of values is odd, the median is given by the value in the \((n 1)/2\) position ( \(n\) is the number of values). The calculation is easy: first of all, we sort the values in increasing order. If we change the highest value into 100, the new mean is moved upwards to 24.2 and it is no longer in central positioning, with respect to the sorted list of data values.Īnother important statistic of location is the median, i.e. the central value in a sorted variable. For example, if we look at the following values: That does not imply that the number of values above the mean is the same as the number of values below the mean. In other words, the values above the mean and those below the mean, on average, are equally distant from the mean. The mean can be regarded as the central value in terms of Euclidean distances indeed, by definition, the sum of the Euclidean distances between the values and the group mean is always zero. The most widely known statistic of location is the mean, that is obtained as the sum of data, divided by the number of values: 16.8 Expressions, functions and arguments.16.2 Installing R and moving the first steps. ![]() ![]()
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