chapter 3. question 3.50 mean=17,776 stan. dev= 12,034 Q1=9900 median=15,532 Q3=

Question

chapter 3. question 3.50 mean=17,776   stan. dev= 12,034 Q1=9900 median=15,532 Q3= 22,500 a) compare the mean and median. also compare the distances ofQ1 and Q3 from the median. explain why both comparisons suggestthat the distribution is right-skewed. (what do they mean by compare?) b) the right skew pulls the stan. dev. up. so a normaldistrubutition with the same mean and stan. dev. wold have a thirdquartile larger the the actual Q3. find the 3rd quartile of thenormal distribution with = 17,776 and =12,034 and compare it withQ3=22,500. chapter 3. question 3.50 mean=17,776   stan. dev= 12,034 Q1=9900 median=15,532 Q3= 22,500 a) compare the mean and median. also compare the distances ofQ1 and Q3 from the median. explain why both comparisons suggestthat the distribution is right-skewed. (what do they mean by compare?) b) the right skew pulls the stan. dev. up. so a normaldistrubutition with the same mean and stan. dev. wold have a thirdquartile larger the the actual Q3. find the 3rd quartile of thenormal distribution with = 17,776 and =12,034 and compare it withQ3=22,500.

Explanation / Answer

In this case, they seem to be looking for a very simpleobservation, that the mean is a bit higher than the median. In a "true" normal distribution, the probabilities are symmetrical;half the observations fall on each side of the mean. That is,the mean is the median. In this problem, the mean isgreater than the median, implying that you have some extra-bigobservations to the right of the median, pulling up themean. . Notice that Q1 is 5632 from the median, and Q3 is 6968 fromthe median.  What does that tell you about the relativemagnitudes of the numbers to the left and to the right of themedian? . Part b is a normal z-score problem, where you need to find thepoint z in the standard normal table such that Pr(x<z) = 0.75,that is, the point z such that 75% of the observations are to theleft of z. Then you translate that z-score from the standardnormal (mean 0 and sigma 1) to the normal distribution you actuallyhave. Do you know how to do that?

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