Math 151 , Spring 2005, Day 4 Mon. Feb. 7 Hit reload to get most current versionAfter class

Errors in my book: Ch4p43 middle; "for men...a narrower broader peak..."
    Ch5p65top: Needs square root sign over formula (later printings are ok(?))
Day 3 (Mon. Feb. 7): Reading:  D&V Ch5, AS Ch5 (D&V, and I, will do medians, quartiles, boxplots first, then mean/s.d.  AS does middles, then spreads, then boxplots.)
We'll start using SPSS next time,Wednesday--have class in the computer lab.  If you're computer-phobic, coming into Mac 101 and trying some ActivStats SPSS exercises ahead of time might help.  No downside except for time lost.  ActivStats only shows how to handle raw data, and Ch.3 text hw problems all involved pre-piled data, harder in SPSS.

Hand in Wednesday (All D&V) Ch5, p. 72  #3,  also make a boxplot.  ("No calculator" means no statistical calculator)  15 Wines 16 Ozone 28 Population growth  p. 107 (review) 18&19 Old Faithful - - - - - - - - - -  Mean/Median.  Will be part of Day6 7a,b,c,Payroll  Also, with c: What measure would be most useful if you wanted to use it to figure the total weekly payroll cost? 6 Sick days + + + + + + + + + +  Start now on a separate page; keep for the next assignments (will be part of Day6): 19, 20 (no computations needed.  19 d may not be decidable from pictures.  Don't worry about it.) 5 Mistake (You can do parts now) 9 Standard deviation Tonight, make  dot plots of each pair on axes with the same unit size, find the mean of each set and mark it with a little ^ (like fig. 5.6 p. 64).  Notice this looks like a good balance point. Leave space to calculate  some standard deviations next time.

Read,  be able to discuss Read Circle questions: email me any more: sievers@wells.edu 25 Caffeine 41 Eye & Hair color 31 Reading scores (f is harder; optional) - - - - - - - - - - -  http://www.whfreeman.com/scc or http://bcs.whfreeman.com/ips5e.  Under Student Categories or Student tools,  choose "Statistical Applets", Mean &Median . (50 points max.)Check out symmetric, skewed, distributions with outliers. How far apart can you get the mean and median? 13 Marriage age.  Ithaca Journal Jan 22, '05 had quiz answers: "How old is the average bride? 24.5 years.... How old is the average groom? 26.5 years." Give some reasons that could account for the big difference between these numbers and the graphed numbers

Optional  ActivStats  lessons on SPSS, in Mac 102:  on AS pp.1-2, 3-1, 3-2, are a gentle introduction (using raw data).  4-2, 4-3 do continuous data.

HW questions?    List of Circle questions.  What did you see, comparing the speed of your hands? will ask Friday

Ch.5 Summarizing distribution info with numbers

Measures of middle (center)
        --Colloquially "average" can refer to any measure of middle, so watch out; be more specific.
   Mean (most common "average"):  Take sum of all observations & divide by how many (n) p. 63
    (Midrange:  Average the maximum & minimum values.  Very sensitive to outliers.)
  Median:half are bigger, half are smaller
      Point on histogram with half the area to the left, half to the right.

Calculating:  Put observations in numerical order (stemplot!).
      Middle one if n is odd, or average the 2 middle  if n is even.
Formula:  Count in how far?  (n+1)/2 places.  (7 1/2 places? go halfway =average the 7th and 8th observations.  Book's method, p.58, is more complicated, same result.)

Computation of quartiles:  Different texts, packages use different methods.
By hand: quick and somewhat dirty:
Take the two halves of the data you got from finding the median.  Find the median of each half, using the same rule as before.  (Detail.  IF you had an even number of observations to start with, the data divides evenly into an upper and a lower half.  IF you had an odd number to start with, you have one in the middle, the median. In this case only, you use the median as part of both halves)
1 3 5 6 8 8 11 20, are n=8 observations.
    Median at (8+1)/2= 9/2=4 1/2th ;  1 3 5 6 | 8 8 11 20, M = 7
 8/2 = 4 in each half: Halves are 1 3 5 6, and 8 8 11 15.  The quartiles are the medians of each half; count in (4+1)/2= 2 1/2.  1 3 | 5 6,  Q₁=(3+5)/2= 4.
8 8 |11 15. Q₃= (8+11)/2= 9.5                                            1 3 | 5 6 | 8 8 | 11 20

1 3 5 6 6 8 8 11 20, are n=9 observations.
     Median at (9+1)/2=10/2=5th ; 1 3 5 6 6 8 8 11 20, M = 6
  The median joins both halves. Each half has (n+1)/2 values.
9+1/2 = 5 in each half: Halves are 1 3 5 6 6, and 6 8 8 11 15.  Quartiles are middle values of each half.
Q₁=5, Q₃= 8                                                                       1 3 5 6 6 8 8 11 20
(This is a dirty method because it doesn't "exactly" divide the data into quarters.  Quick? Yes.  Tukey did a variation on this, throwing away the median instead of giving it to each half.  He called them "Hinges" to avoid fights over the "quartile" name.  People who took the course out of Moore, Basic Practice, before this term, learned that method.)

INTERQUARTILE RANGE = IQR= Q3 - Q1.
=The range of the middle half of the observations.  Resistant to outliers!
       9.5 - 4 = 5.5 for the set of 8.   8 - 5 = 3 for the set of 9.

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"Showing outliers" Outliers can make a boxplot whisker extend deceptively beyond the bulk of the data.
      Make the whiskers to the last item in the "main mass" of the data.
       Put a dot or a star for each outlier,  beyond the whisker end.
   How do we decide what's an outlier?  (Rule of thumb; esp. for computers.)
      Fence: Define "outlier" as a value farther out than 1.5 IQR  from the Quartiles.
          (Q1 - 1.5 IQR is lower fence, Q3 + 1.5 IQR is upper fence.
                For the set of 9, 1.5 IQR = 4.5.  Fences are 5 - 4.5 = .5, and 8 + 4.5 = 12.5.
                   So 20 lies outside the fence, and the whiskers & box  should go from 1 to 11 (largest inside the fence)
        (Dot or *?  Tukey:  Dot ·between 1.5 and 3 IQR's out, * if more than 3 IQR's out. By hand, I don't care.)
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