Assignment 17

course Mth. 152

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017. `query 17

Liberal Arts Mathematics II

04-19-2008

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11:58:39

**** query problem 13.4.12 z score for KG's rebounds (.4 from bottom range 10-13)

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RESPONSE -->

I could not find this problem in the book.

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12:01:55

** The z score for KG is his total number of rebounds minus the mean average number of rebounds for all the players and then divided by the standard deviation. In KG' s case:

z = (489 - 538.2) / 38.8 = -1.3 **

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RESPONSE -->

I wasn't able to find tihs problem in the book. I didn't know how to work it with the number you gave us. I see how you worked it but I still cannot figure out where the numbers came from, sorry.

The mean number of rebounds was 538.2 and the standard deviation was 38.8; KG has 489, which was 1.3 standard deviations below the mean.

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12:05:52

query problem 13.4.30 midquartile same as median? (Q1+Q3)/2

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RESPONSE -->

No. The Median is obtained by adding all your number and then dividing by the number of numbers you have (an average of your numbers). The midquartile is the two centered numbers added and then divided by 2.

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12:07:45

** If the median is the actual number in the middle, the it's not necessarily equal to the mean of the first and third quartile. There are different ways to see this.

For example suppose that in a large set of numbers, the median number is at least 2 greater than the next smaller number and 2 smaller than the next greater number. Then if all the other numbers stay the same, but the median is increased or decreased by 1, it's still in the middle, so it's still the median. Since all the other numbers stay the same, the first and third quartiles are the same as before, so (Q1 + Q3) / 2 is still the same as before. However the median has changed. So if the median was equal to (Q1 + Q3) / 2, it isn't any more. And if it is now, it wasn't before. In either case we see that the median is not necessarliy equal to the midquartile.

To be even more specific, the median of the set {1, 3, 5, 7, 9, 11, 13} is 7. The median of the set {1, 3, 5, 8, 9, 11, 13} is 8. The midquartile of both sets is the same, so for at least one of the two sets (namely the second, as you can verify for yourself) the median and the midquartile are different. **

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RESPONSE -->

I got the median and mean mixed up but I know they aren't the same.

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Q2 is the median, which is not necessarily in the exact middle between Q1 and Q3.

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Good responses. See my notes and let me know if you have questions. &#