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Quartiles are useful, but they are also somewhat limited because they do not take into account every score in our group of data. To get a more representative idea of spread we need to take into account the actual values of each score in a data set. The absolute deviation, variance and standard deviation are such measures.
The absolute and mean absolute deviation show the amount of deviation (variation) that occurs around the mean score. To find the total variability in our group of data, we simply add up the deviation of each score from the mean. The average deviation of a score can then be calculated by dividing this total by the number of scores. How we calculate the deviation of a score from the mean depends on our choice of statistic, whether we use absolute deviation, variance or
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.
Perhaps the simplest way of calculating the deviation of a score from the mean is to take each score and minus the mean score. For example, the mean score for the group of 100 students we used earlier was 58.75 out of 100. Therefore, if we took a student that scored 60 out of 100, the deviation of a score from the mean is 60 - 58.75 = 1.25. It is important to note that scores above the mean have positive deviations (as demonstrated above), whilst scores below the mean will have negative deviations.
To find out the total variability in our data set, we would perform this calculation for all of the 100 students' scores. However, the problem is that because we have both positive and minus signs, when we add up all of these deviations, they cancel each other out, giving us a total deviation of zero. Since we are only interested in the deviations of the scores and not whether they are above or below the mean score, we can ignore the minus sign and take only the absolute value, giving us the absolute deviation . Adding up all of these absolute deviations and dividing them by the total number of scores then gives us the mean absolute deviation (see below). Therefore, for our 100 students the mean absolute deviation is 12.81, as shown below:
absolute deviationAnother method for calculating the deviation of a group of scores from the mean, such as the 100 students we used earlier, is to use the variance. Unlike the absolute deviation, which uses the absolute value of the deviation in order to "rid itself" of the negative values, the variance achieves positive values by squaring each of the deviations instead. Adding up these squared deviations gives us the sum of squares, which we can then divide by the total number of scores in our group of data (in other words, 100 because there are 100 students) to find the variance (see below). Therefore, for our 100 students, the variance is 211.89, as shown below:
Review by
Nicole Zdeb
— Published on December 3, 2012 Tags:
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Forty years have passed since L’Arrière-pays was published in French to nearly instant acclaim. It first appeared as part of a collection titled Les sentiers de la creation (The Paths of Creation, 1972) that included contributions by Claude Lévi-Strauss, Roland Barthes, Pablo Picasso and Francis Bacon. Now that Seagull Books has ushered the work into English, there can be no doubt that this was a book worth waiting for. The Arrière-pays is an immersion in the heady waters of a profound aesthetic consciousness.
In it, Yves Bonnefoy threads memory, thoughts on art and architecture, dreams, the plot of a favorite book, and two unfinished novels—all through an analytic lens that borrows from language philosophy, Freud, and modernism. He traces the branching of an idea that sparked to life in childhood: that of the l’arriere-pays , a not here that is radiant and transformative; a place of symmetries; an idealization with Platonic overlays. The phenomenon of this lived world, art and nature, reveal this deferment of perfection and trigger the yearning for Other that is so much a part of love. This book could be viewed as a moral tale of how infatuation with a concept, however alluring and seemingly benign becomes dangerous when it leads you out of love with this world.
Bonnefoy recognizes this temptation into delusion and grapples with it with spiritual grace and intellectual rigor. L’Arri è re-pays is, as Bonnefoy says in the preface, “the great phantasm”:
I have often experienced a feeling of anxiety, at crossroads. At such moments it seems to me that here, or close by, a couple of steps away on the path I didn’t take and which is already receding—that just over there a more elevated kind of country would open up, where I might have gone to live and which I’ve already lost.
This book is a study of inquietude, its signs and the system of specialized knowledge, or gnosis, that they represent. Bonnefoy states, “In L’Arrière-pays —and this is what sets it apart from my other books—I took the risk of confronting head on a particular temptation I was prey to, arguing that I had to struggle with it, saying that I had struggled with it, imagining that I had triumphed over it.”
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