Math 151 , Fall 2005, Day 6  Wed. Sept 7 Hit reload...After class in Green

What's due today?  The Chapter 3 HW (Day 4's assignment).
What's due Friday?  Nothing, but hand in SPSS exercises that you've finished.
All of Chapter 5 HW is postponed again. Work on SPSS (Day 5 HW).  You know all the statistics except for the added questions in #E.  If you've read the book and the handout (page 3) you can get the desired numbers off the output without thinking much what they mean. (IQR = InterQuartile Range).  Write the discussion after the next lecture.
Errors in my book: Ch4p43 middle; "for men...a narrower broader peak..."
    Ch5p65top: Needs square root sign over formula (later printings are ok(?))
Day 6 (Wed. Sept 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.)
Nothing new to hand in for Friday.  All of this is postponed.
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. 
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, do the parts that you can; keep for the next assignment :
19, 20 (no computations needed.  19 d may not be decidable from pictures.  Don't worry about it.)
5 Mistake 
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.  Also, make a dot plot of  #10b set 2 (10, 50, 60, 70, 110).  Which of the data sets in problem 9 does it most resemble?		 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/ips  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.
Email list: Math151@wells.edu
Cluster:  Tell everyone your name, even if you think they know it.
   Check for Homework questions? Remaining #s on board.
SPSS problems?  Don't postpone...
Leftover HW questions?   What did you see, comparing the speed of your hands?    List of Circle questions.

Ch.5 Summarizing distribution info with numbers  See Day 4 for details

Measures of middle
          Mean  x-bar   (Midrange)  Median: Count in how far? (n+1)/2 places.  Start here Friday
Spread :(Standard Deviation s,Next lecture.)  Range:  Max - Min.  Interquartile range IQR.
     QuartilesDivide data into quarters: 1st quartile Q1:  = 25th percentile.
                   3rd quartile Q3:   = 75th percentile.

Computation of quartiles:  By hand:
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)
Five-number summary:  min, Q1, Median, Q3, max.
INTERQUARTILE RANGE = IQR= Q3 - Q1.
=The range of the middle half of the observations.  Resistant to outliers!
Box (and whisker) plot:  &&"Plain vanilla"
The box spreads over the middle half (Q1 to Q3), the whiskers over the lowest and highest quarters (Min to Q1, Q3 to Max).  Each section shows the spread of 1/4 of the data: the longer the section the thinner the data must be spread in there
"Showing outliers" 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.    Fence: Define "outlier" as a value farther out than 1.5 IQR  from the Quartiles.  <>Boxplots shine at comparing distributions conditioned with several categories .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mean vs. Median
Mean (most common "average"):  Take sum (aggregate) of all observations and divide by how many (n)
        Metaphors.  1) Center of gravity, balance point of histogram.
                2) Slice off bits from the big and add to the little till everyone has the same.
                    (Or "aggregate"--total-- it all and portion it out evenly.)
        Outlier or long tail will pull mean in that direction (think seesaw balancing)  "Sensitive" to outliers, skewness.
        Especially useful: 1) For symmetric, tidy distributions
            2) When metaphor 2 makes sense--looking for "fair share" of a total.
    Median: half are bigger, half are smaller
        Point on histogram with half the area to the left, half to the right.
                "Resistant to skewness and outliers"--trimming off ends will make little difference in median value.
        More "typical" than mean, if there is skewness or outliers.
     (Badly bimodal distribution?--"middle" doesn't mean much. Give values at modes.
         Extremely skewed or J-shaped?  Mode (value at peak) might better tell most typical)
    Symmetric distribution: mean = median .  Skewed:  mean pulled to long-tail side of median.
Investigate differences:  Activstats 5-3.
David S. Moore's websites http://www.whfreeman.com/scc or http://bcs.whfreeman.com/ips5e.  Under Student Categories or Student tools,  choose "Statistical Applets", Mean &Median . Check out symmetric, skewed, distributions with outliers.
Sievers home  Math151-Fall05/Dayf6.htm  1:30pm 9/7/05
This page belongs to Sally Sievers who is solely responsible for its content. Please see our statement of responsibility.