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E7 Homework sheet for mean-variancerandom
copy/pastegrade copy/sortis A?is B?is C?is D? Averages:absolute distributionf(x) = relative distributionmodal grade = F(x) = cumulative distributionmedian grade =x (midpoint of range)x*f(x)
m = meanx m (x m)^2(x m)^2*f(x)
variance standard deviationx^2 x^2 *f(x) second moment moment difference8Questions. You must explain why your answer is correct.
k1. Suppose that a distribution has a kurtosis of 5. Is it reasonable to think this distribution is normal?\2. Would you expect the distribution with kurtosis 5 to have many outliers, or few outliers?g3. Suppose a distribution has a skewness of -1. Is it reasonable to think this distribution is normal?{4. Would you expect the mean of the distribution with skewness -1 to be larger than, smaller than, or equal to, the median?5. Fill in the American-style grade distribution below to get the maximum possible kurtosis. Feel free to use more cells for auxiliary (helpful, related) computations.ABCDFgrade pointsrelative frequencykurtosis6. Fill in the American-style grade distribution below to get the maximum possible skewness. Feel free to use more cells for auxiliary (helpful, related) computations.skewness7. Take three random distributions. (You may need to recalculate the sheet to get a new random distribution. F9 is commonly used for this command. If that doesn't work, read the documentation for your program.) For each, compute the mean and variance by hand. (You will need to do this on the midterm.) Estimate the standard deviation. All computations may be accurate to the nearest integer. You do not need to show your work for this problem but you should add cells to automatically check your work after you do the computations.meanvariancestandard deviationNote scale!random absolute distributioncopy/paste 1copy/paste 2copy/paste 3k8. A study of people who drove from Tsukuba to Kyoto showed that their driving time was an average of 11 hours, with a standard deviation of 1.5 hours. Would you be surprised to hear that someone completed the trip in 14 hours? Would you find it more or less surprising if the trip took 8 hours? Why do you think I chose 14 hours and 8 hours for this question? 9. A study of students at a certain university showed that women had an average height of 160cm with a standard deviation of 10cm, while men had a mean height of 168cm with a standard deviation of 12 cm. Is a woman of 168cm more unusual or less unusual than a man of 160cm in this group?
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