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This difference is called the deviation of the observation Yi from the mean μ. Based on the definition of the mean for a finite population, it is easily seen that “the sum of the deviations of all data points from the mean of the finite population” is zero. In case we a sample on our hands, the deviation from the mean of the sample X can be found as Yi – X. 8). We now turn to how to compute the variance and the standard deviation of a finite population. e. N ∑ (Y − µ ) σ2 = i i =1 2 . N Thus, the standard deviation, σ will be given by N σ= ∑ (Y − µ ) i i =1 2 N .
2. The Mode is the most frequent data point in the sample. The mode is considered to be the least informative measure in the central tendency measure. Generally speaking there are two cases where the mode is useful. g. Hair color, Geographical data) it should be obvious that one can count the most frequent or popular class, while the mean and median cannot be computed. For Example, What meaning would a statement like “the average washing machine is a Maytag” have? Secondly, one may also cite the mode or modes of a distribution along with the mean and median.
15, we see that minimum = 7, and the maximum = 34. Therefore the range is given by R = 34 – 7= 27. More specifically, for n observations which are ordered from the smallest Y1 to the largest Yn the range is: R = Yn – Y1. The range does not tell us how the observations are distributed between the smallest and the largest ones. The only information we really have from the range is the distance between the smallest and the largest measurements. As such, the range statistic is not a measure of dispersion of all the observations.
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