solution-2%5B1%5D - 1. How do you calculate and interpret...

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1. How do you calculate and interpret range, mean and standard deviation? Let } ,... , { 2 1 n x x x X = Range =max(X)-min(X), that is, the maximum element in X minus the minimum element in X. Mean = X = n x n i i = 1 . Standard deviation=s= n X x n i i = - 1 2 ) .( 2. What does knowing a measure of variation (range or standard deviation) tell you about the data? The range tells you what value do the data vary, or how large/small do the data reach. The standard deviation tells you how far the data deviates from the center of the data on average. 3. What does the Empirical Rule and/or Chebychev’s Rule tell us? Both rule/theorem tell us that most of the data are within 2 or 3 times of standard deviation, s, from the sample mean. Or in other words, most of data are well centered around the sample mean. 4. What percent of the data fall between each quartile? 25%. 5. What does it mean to say the data is right-skewed (or positively skewed)? More data are larger than the center of the measurement (mean). Or, more than 50% of the data is larger than the center of the measurement (mean).
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6. When is median useful, as opposed to using the mean? When the data is skewed irregularly, median is more useful. For example, if we have a data set of {0,1,2,3,4,5,6,7,10000}, the median is 4, and the mean is 1114.2. Since the data is most around 4, median is more useful in this situation. 7. How do you calculate probability using the various rules? For continuous random variable/probability, we can calculate probability of the standard form P(X<x) by checking the cdf, since if F(x) is the cdf of a random variable X, the F(x)=P(X<x). For P(X>x), we can transform it to 1-P(X<x), and then use cdf to find out P(X<x) For P(x1<X<x2), we transform it to P(X<x2)-P(X<x1), and use cdf. For discrete random variable/probability, we can calculate probability of the standard form P(X<=x) by checking the cdf, since if F(x) is the cdf of a random variable X, the F(x)=P(X<=x). For P(X>x), we can transform it to 1-P(X<=x)=1-F(x).
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solution-2%5B1%5D - 1. How do you calculate and interpret...

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