Unit 1 Exploring Data: Distributions Topic 2 Data, Variables, and Calculators (page 19)

OVERVIEW In the first topic you encountered many sets of data and explored the notion of variable and its distribution. This topic introduces you to using your TI calculator to analyze data. It also leads you to perform elementary manipulations of variables and to ask whether the data at hand satisfactorily address the question or issue one has in mind.

Do the Preliminaries (pages 19 to 21)

Essential Question How can the graphing calculator be used to analyze data?

Calculator Introduction. Switch to TI-Smart View calculator for an overview! Then copy lists and program.

Lists you will need in your calculator for this topic: ATTEN BEER BSIZE CAPAC CAPS FEWER HOTD INDEX INJUR KIDS MEN MORE PARK PARTI PROG SAT SODA SSIZE TIX WOMEN … and the program Dotplot.

Essential Question How can the graphing calculator be used to analyze data?

Activity 2-1 Scrabble Names (pages 21 to 25)

Switch to TI-Smart View calculator!

b. The distribution of the dotplot for the number of letters is … Lowest number of letters is 5 (Tukey) Most number of letters is 11 (Nightingale) Second most is 9 letters (Blackwell) Centered around 6 letters More have 6 letters in their name

c. The distribution of the dotplot for the total points is… Lowest number of points is 9 (2 statisticians) Most number of points is 20 (Blackwell) Second most is 16 points (Nightingale) High number(s) of points may be outlier(s) Most are between 7 and 12 letters

d. The statistician with the most … Letters is Nightingale with 11 letters. Points is Blackwell with 20 points. These are NOT the same person!

e. The statistician with the fewest … Letters is Tukey with 5 letters. Points are Gosset and Galton with 9 points each. These are NOT the same person!

(f) Name# of letterstotal ptsratio Nightingale1116 Tukey512 Fisher612 Blackwell920 Neyman611 Gosset67 Norwood711 Pearson79 Deming610 Galton67

(f) Name# of letterstotal ptsratio Nightingale Tukey Fisher Blackwell Neyman Gosset Norwood Pearson Deming Galton671.17

The distribution of the dotplot for the ratio of points to letters is… Fairly evenly spread out Ranges from 1 to 2 points per letter

h. The statistician with the highest ratio is … Tukey with a ratio of 2.4 points / letter. This statistician’s ratio is so high, because Tukey has fewer letters but the letters are worth higher points.

Essential Question How can the graphing calculator be used to analyze data?

Activity 2-2 Gender of Physicians (pages 25 to 29)

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(b) SpecialtyIndexWomen 1. internal medicine1632, pediatrics2825, family practice1016, colon/rectal surgery aerospace surgery thoracic surgery3613

(c) The aspect of the gender breakdown that the “number of women” variable does not take into account is … The number of physicians in each field. It is leaving out the number of male physicians.

(d) SpecialtyIndexWomen % 1. pediatrics % 2. medical genetics % 3. child psychiatry539.06% 35. neurological surgery184.42% 36. orthopedic surgery243.30% 37. urological surgery372.63%

(e) Do the lists in part (b) and part (d) agree?______ NO! If not, explain. The ratios of women to men differ.

Follow the textbook directions for parts (f), (g), (h), and (i). Part (f) is for a “typical” number of women physicians. Part (g) is for a “typical” percentage of women physicians. Part (h) name specialty more than your part (f) but smaller than your part (g). Part (i) name specialty fewer than your part (f) but larger than your part (g).

(j) The distribution of the dotplot for the percentages of women physicians is… Fairly mound shaped Minimum 3% and maximum 46% Clustered around 20 to 25% Peak at 25%

(k) In summary … it is difficult to compare the counts (numbers) since the numbers vary greatly from specialty to specialty.

When a variable involves counting the number of people or objects that belong in categories of different sizes, rates or percentages often provide a more appropriate variable to study.

Assignment Activity 2-8: Broadway Shows (pages 36 & 37) Assignment Activity 2-7: Hazardousness of Sports (pages 35 & 36) How can the graphing calculator be used to analyze data?

Essential Question How can the graphing calculator be used to analyze data?

Activity 2-3 Fan Cost Index (pages 29 & 32)

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(a) The team with the highest FCI and its value … N.Y. Yankees $ The team with the lowest FCI and its value … Montreal Expos $87.87 Now the Washington Nationals.

(b) Comment on the distribution.

Minimum $87.87 (Expos) and maximum $ (Yankees) Most teams between $90 ($120) and $140 Very few outliers – mostly on the higher end of distribution (N.Y. Yankees & Boston Red Sox)

Follow the textbook directions for parts (c), (d), and (e). Part (c) is your team’s (from Preliminaries) FCI and position relative to other teams. Part (d) is for the people with whom you would attend a game (or concert). Part (e) is like part (a) but for YOUR new equation … MCI.

(f) The ballpark with the highest charge for a small soda is … N.Y. Mets which costs $3.50. The ballpark with the lowest charge for a small soda is … Phila. Phillies which costs $1.25.

(g) It is misleading to compare the costs of a small soda or a small beer in the different ballparks because …. the size “small” is relative to the ballpark’s drink size.

(h) The ballpark with the highest soda price per ounce is … Boston Red Sox which costs $0.18 /oz. The ballpark with the lowest soda price per ounce is … Montreal Expos which costs $0.8 / oz. Now the Washington Nationals.

Assignment Activity 2-6: Fan Cost Index (continued) (pages 34 & 35) Assignment Activity 2-13: Driver Safety (page 40) How can the graphing calculator be used to analyze data?

Essential Question How can the graphing calculator be used to analyze data?

Activity 2-4: State ’ s SAT Averages (pages 32 & 33)

The state with the highest average SAT score is ________________________. The state with the lowest average SAT score is ________________________. Iowa (1194 average & 5% taken) South Carolina (951 average & 61% taken) (a)

… and I noticed that the percentages of the students taking the exam in those states was … high for the lowest average SAT scores and low for the highest average SAT scores. (b) Be sure you have the lists named SAT, MORE, and FEWER!

Switch to TI-Smart View calculator!

… than 25% of the students take the SAT

I noticed that the distributions of the SAT averages for these two groups was … completely centered around two (2) different values (1000 & 1120), with very little overlap. I believe the reason for this pattern is that … the states with the higher percent takers have more non-college bound students taking the SAT exam.

c)Is “SAT average” a good variable for deciding how well a state educates its students? NO! [explain] As more students take the exam, it is likely this will reduce the overall average.

d)In terms of SAT average, my home state of Pennsylvania compares with the rest, in that …

… than 25% of the students take the SAT

d)In terms of SAT average, my home state of Pennsylvania compares with the rest, in that … they are at the lower end of the distribution with a score of 992. In terms of percentage of students taking the test, my home state of Pennsylvania compares with the rest, in that … they are at the upper end of the distribution with a percent of 71%.

WRAP-UP This topic has given you more experience with data and with the ideas of variability and distributions. You have used your TI calculator to analyze data, and you also seen that manipulating a variable, for example by converting it to a rate, is often necessary. You have begun to consider the conclusions one can draw from statistical studies as related to the variables measured.

In the next topic you will study distributions of data further by considering visual displays other than the dotplot. You will also develop a checklist of features to look for when describing distributions verbally.

Your topic is due! Quiz on Topic 2: Activity 2-5: Scrabble Names (continued) (page 34) NOTE: You must put the data from the Preliminaries in your calculator for this quiz. How can the graphing calculator be used to analyze data?