HW assignment Day4 (From Moore unless
Timeplot, p.23-5. You will need to be able to recognize cyles and trends, not make timeplot by hand. (We'll make them in SPSS later.)
Now Ch.2 thru p. 43.(mean/median) Do Check p. 58 2.15, 16, 18. PLEASE Read ahead! pp. 43-49 (5#summary/boxplot) Do Check p.59 17,19,20 Read 55-6, "Organizing...". then: Finish Ch. 2 pp. 49-55(standard deviation, using technology). ("Check" problems: skip 2.21, do 22-24)
Do the 5-number summaries required here by hand (with a calculator if needed for means, finding middles between 2 numbers).
Hand in next class.:
(note,The first set of problems is copied from Day
(postponed). Label everything Day 4.)
A. You are driving on the thruway from Syracuse to Rochester and keep track of how many vehicles you pass and how many pass you. You find that these 2 numbers are the same. Your speed on the thruway is: (a) the Mean speed of the cars, (b) the Median speed of the cars, (c) the Modal speed of the cars. Choose one, and justify your choice.
Text material for Questions for
rest of this page
YES:DON'T hand in any of
below yet, but :
+ + + +Another + + + +
discuss (be able to answer in class)
Ch. 2 Questions--mean/median
p. 62, 2.37 Thinking about means Look at the answer in the back for the mean..
p. 62, 2.38 Thinking about medians
- - - - - -
P. 61, 2.34 (mean/median play, with Applet)
p. 63, 2.41, 42 (more play, with pencil--and/or open the Applet, One Variable Statistical Calculator, type data in at the Data tab, see
Sign in on the clipboard. .
--Compare HW with others, tell me unanswered questions, write #s on the board.
--Friday we'll meet in computer lab Mac 101 for intro to SPSS. At that point we'll be using it heavily for about 3 1/2 weeks, then not again till the very end of term. SPSS for you??
Lab session offered 10:30 & 11:30. Sign up Wed. (Not binding)
Class members Math151@wells.edu (??)
HW questions? Day 3
http://bcs.whfreeman.com/bps5e for 1.35, Doctors (they round, so 798 goes on as 8|0. Yours (truncating) should look a little different, but match a histogram.)
http://bcs.whfreeman.com/ips7e/ CO2 per cap. by country. The data here is a little different from yours, but should be same rough shape. Different years? (I used the references and tried to track them down, but the data didn't match up perfectly to any source.)
Overview--"Variability happens, but things
down in long run." Notes, Day 2
Timeplots. Trend, cycles Beer1
Measures of Middle Mean/ median. Notes, Day 3
Measures of Spread (dispersion, variability) distributions with different spreads
Range: largest - smallest. Resistant? NO! Two observations carry all the info; the rest could be anywhere.
Dot plots of 3 distributions, all with
We need measures of spread that will better take into account all the observations:
Quartiles, five-number summaries, boxplot, InterQuartile Range.
. .. .
(Variance), Standard deviation.
Start here Wednesday
Quartiles Divide data into quarters: 1st quartile Q1: 1/4 below, 3/4 above. = 25th percentile.
(2nd quartile= median = 50th percentile)
3rd quartile Q3: 3/4 below, 1/4 above. = 75th percentile.
Computation of quartiles: Different texts, packages use different methods.Five-number summary: min, Q1, Median, Q3, max. (1, 4, 6, 9.5, 20 for the set of 9 above)
By hand: We'll use Tukey's quick and dirty: (he called them "hinges")
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. No problem. IF you had an odd number to start with, you have one in the middle, the median. In this case only, you throw the median away, and use the remaining 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 20. The quartiles are the medians of each half; count in to (4+1)/2= 2 1/2th place.
1 3 5 6, Q1=(3+5)/2= 4. 8 811 20. 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 8 8 11 20, M = 6
Throw away the median. Now we have an even number again, 8 numbers
8/2 = 4 in each half: Halves are 1 3 5 6, and 8 8 11 20. Continue as before. (This is a dirty method because it gives the same quartiles for both these data sets. Quick because computation is minimal and simple.)
1 3 | 5 66 8 8 | 11 20
statistical problem: Four-step process
55-7, & inside front cover)
State: the issue to be explored, question to be addressed (real-world) (In HW problems, often already stated.)
Plan: What statistical tools, measures, analyses should we use to answer the question?
Solve: Carry out the process. (May need to back up & try again. You decide on mean, s.d., but stemplot shows badly skewed? go back and decide on 5#summary instead.)
Conclude: Give the conclusion as it addresses the real-world question/issue.
Any time left?? .won't be probably. Begin p. 57, 2.13 in class in pairs (or 3's). Decide what analyses to do; start doing them (make a copy for each person, if you won't be working together outside of class.)