Investigation 2: “Tipping Point” connectors (due Wed, Jan 11)

You may work with one other person on this assignment, handing in one report with both names.  Word-processed reports are preferred to hand-written ones.  Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

Based on the idea presented in Malcolm Gladwell’s book The Tipping Point, I asked each of you to determine how many people you know with last names appearing on a list of 250 names taken randomly from the Manhattan phone book. The resulting data for 99 students are:

6 7 8 10 10 10 10 11 11 12 13 14 14

15 15 15 15 16 16 16 17 18 18 18 19 19

19 20 20 20 21 21 21 21 22 23 23 23 24

24 25 26 27 27 27 27 27 28 29 31 33 33

33 33 33 33 35 35 36 36 36 36 36 36 37

37 39 40 40 40 41 44 45 45 46 47 48 48

49 49 49 50 50 53 54 62 65 65 67 70 72

82 85 85 86 98 107 127 139

(a) Produce (by hand) a stem-and-leaf plot of these data.

(b) Write a paragraph commenting on the distribution of these data (numbers of acquaintances from this list of names, for the students in my two sections of our class). [Hint: Remember the checklist of features to look for, and be sure to relate your comments to the context.]

The data appear in C1 of the Minitab worksheet GladwellConnectorData.mtw.

(c) Calculate (and report) the mean and standard deviation of these data. Also determine what percentage of these students’ scores fall within one standard deviation of the mean. Is this value close to 68%, as the empirical rule would predict? Should it be? Explain.

(d) Determine (and report) the five-number summary of these data. Use this summary to conduct (by hand) a check for outliers. Show the details of your calculations, and identify all outliers (if any) that you find.

(e) Produce (and submit) a boxplot of these data.

Gladwell wrote: I have given this test to at least a dozen groups of people. One was a freshman World Civilizations class at City College in Manhattan. The students were all in their late teens or early twenties, many of them recent immigrants to American, of middle and lower income. The average score in that class was 20.96, meaning that the average person in the class knew 21 people with the same last names as the people on my list. I also gave the test to a group of health educators and academics at a conference in Princeton New Jersey. This group was mostly in their 40's and 50's, largely white, highly educated--many had PhD's--and predominatly upper income. Their average score was 39. Then I gave the test to a relatively random sample of my friends and acquaintances, mostly journalists and professionals in their late 20's and 30's. The average score was 41. These results shouldn't be all that surprising. College students don't have as wide a circle of acquaintances as people in their 40's. It makes sense that between the age of 20 and 40 the number of people you know should roughly double, and that upper-income professionals should know more people than lower-income immigrants. In every group there was also quite a range between the highest and the lowest-scorers. That makes sense too, I think. Real estate salesmen know more people than computer hackers. What was surprising, though, was how enormous that range was. In the college class, the low score was 2 and the high score was 95. In my random sample, the low score was 9 and the high score was 118. Even at the conference in Princeton, which was a highly homogenous group of people of similar age, education and income--who were all, with a few exceptions, in the same profession--the range was enormous. The lowest score was 16. The highest score was 108. All told, I have given the test to about 400 people. Of those, there were two dozen or so scores under 20, and eight over 90, and four more over 100. The other surprising thing is that I found high scorers in every social group I looked at. The scores of the students at City College were less, on average, than adult scores. But even in that group there are people whose social circle is four or five times the size of other people's. Sprinkled among every walk of life, in other words, are a handful of people with a truly extraordinary knack of making friends and acquaintances. They are Connectors.

(f) Write a paragraph commenting on how our class data compares to Gladwell’s observations about other groups on whom he has conducted this activity.