Chapter 2: Problem 75
What is advantage of the range as a measure of variability?
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Chapter 2: Problem 75
What is advantage of the range as a measure of variability?
These are the key concepts you need to understand to accurately answer the question.
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Why do we square the deviation from the mean before adding them to compute the variance?
Refer to the Southern Economic Journal (Apr. 2008) study of Ph.D. programs in economics, Exercise 2.129 . The authors also made the following observation: "A noticeable feature of this skewness is that distinction between schools diminishes as the rank declines. For example, the top-ranked school, Harvard, has a \(z\) -score of \(5.08,\) and the fifth-ranked school, Yale, has a z-score of 2.18 , a substantial difference. However, .. the 70th-ranked school, the University of Massachusetts, has a z-score of \(-0.43,\) and the 80 th-ranked school, the University of Delaware, has a z-score of -0.50 , a very small difference. [Consequently] the ordinal rankings presented in much of the literature that ranks economics departments miss the fact that below a relatively small group of top programs, the differences in [overall] productivity become fairly small." Do you agree?
Refer to the American Journal of Physical Anthropology (Vol. 142,2010 ) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise \(2.65(\mathrm{p} .90) .\) The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted from skulls are reproduced in the table.$$ \begin{array}{lcc} \hline \text { Data on Dentary Depth (mm) of Molars } & \\ \hline 18.12 & 15.76 & 13.25 \\ 19.48 & 17.00 & 16.12 \\ 19.36 & 13.96 & 18.13 \\ 15.94 & 16.55 & 14.02 \\ 15.83 & 15.70 & 14.04 \\ 19.70 & 17.83 & 16.20 \end{array} $$ a. Find the range of the data set. If the largest depth measurement in the sample were doubled, how would the range change? Would it increase or decrease? b. Find the variance of the data set. If the largest depth measurement in the sample were doubled, how would the variance change? Would it increase or decrease? c. Find the standard deviation of the data set. If the largest depth measurement in the sample were doubled, how would the standard deviation change? Would it increase or decrease?
Between the mean and the median, which one is affected by the minimum and maximum values of the observed data?
Graph the relative frequency histogram for the 500 measurements summarized in the accompanying relative frequency table.$$ \begin{array}{cc} \text { Class Interval } & \text { Relative Frequency } \\ \hline .5-2.5 & .10 \\ 2.5-4.5 & .15 \\ 4.5-6.5 & .25 \\ 6.5-8.5 & .20 \\ 8.5-10.5 & .05 \\ 10.5-12.5 & .10 \\ 12.5-14.5 & .10 \\ 14.5-16.5 & .05 \end{array} $$
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