# STAB22H3 Lecture Notes - Lecture 4: Standard Deviation, Quartile, Minimax

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## Document Summary

10% of the observations and compute the mean of the remaining 80%. Similarly, we can compute 5%, 20%, etc. trimmed mean: trimming eliminates the effect of a small number of outliers. Compute the 10% trimmed mean of the data given below: Solution: arrange the values in increasing order: a. There are 20 observations and 10% of 20 = 2. 2: hence, discard the first 2 and the last 2 observations in the ordered data and compute the mean of the remaining 16 values, mean = 19. 812. Properties of standard deviation: s measures the spread about the mean and should be used only when the mean is chosen as the measure of center, s = 0 only when there is no spread. This happens only when all observations have the same value. Otherwise, s > 0: s, like the mean, is not resistant to extreme values. A few outliers can make s very large.