Days 31 - 40

Sanderson M. Smith


Day #31:

"Every problem that I solved became a rule which served afterwards to solve other problems."


Begin construction of spreadsheet for analysis of California's Lottery Game SuperLOTTOPlus. Details provided in class.

Day #32:

"We make decisions in the dark of data."


Review day: Students given two problems to work out in class.

Problem #1: You pay $100 to enter a room. You get to pick a card from a thoroughly shuffled deck. If card is a spade, you win $120. If card is a red king, you win $200. If card is the ace of diamonds, you win $1,000. Calculated your expected payback and your expected gain.

Problem #2: Arrow spinning on a wheel ...Circle divided into five sectors. If arrow lands in

sector with central angle 1o, you must pay $10,000.
sector with central angle 2o, you win $15,000.
sector with central angle 3o, you must pay $1,000.
sector with angle (1/2)o, you win $100,000.
the remaining sector, you must pay $100.

Calculate your expectation in terms of gain or loss.

Day #33:

"The plural of anecdote is not data."


Test day.

Day #34:

"The pure and simple truth is rarely pure and never simple."


Construct a spreadsheet displaying scatterplots relating to data for the Cate class of 1988. Spreadsheet should include scatterplots for

(1) X = best Verbal SAT vs. Y = 10-11-12 GPA


(2) X = best Math SAT vs. Y = 10-11-12 GPA.

In each case, the equation of the least-squares regression line should be produced along with the value of R2.

Day #35:

"Chance favors prepared minds."


Complete spreadsheet assigned on Day #35. Class activity (construction of a least-squares regression line) utilized the data in problem 3.56 (page 179). Scatterplot will give some idea about the relationship between investments in the United States and investments overseas.

Day #36:

"A small error in the beginning is a great one in the end."


For the data relating to calories for the three hot dog types listed on page 59:

(1) Construct parallel box-whisker plots to compare the three data sets.

(2) For each set, calculate the mean and standard deviation.

(3) For each data set, calculate the percentage of items that are (a) within 1 standard deviation of the mean; (b) within 2 standard deviations of the mean; (3) within 3 standard deviations of the mean.

Day #37:

"Learning is the only thing the mind never exhausts, never fears, and never regrets."


Data collected in class. D = day of birth (1-365), A = arm span (inches), F = finger span (inches), and H = height (inches). Look at scatterplots of the following sets: {(A,H)}, {(A,F)}, {(D,H)}, and {(F,H)}. Determine if you can reasonably predick the second variable from the first. Calculate the least-squares regression line and the values of r and r2 for each set.

Day #38:

"How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality."


Complete the set of scatterplots described in Day #37. During the class period activities were devoted to calculating and understanding the concept of a z-score. (Reference page 94 in text.), If x is an observation from a distribution that has mean m and standard deviation s, then the standardized value of x (often called the z-score of x) is

z = (x - m )/ s

Day #39:

"We used to think that if we know one, we knew two, because one and one are two. We are finding that we must learn a great deal more about the word 'and' ."


Find a real set of numerical data containing at least twenty items. Put these into a spreadsheet and calculate mean and standard deviation. In an introduction, clearly identify what the values represent. Calculate z-value for each item. Calculate mean and standard deviation for z-values (should be 0 and 1, respectively). Produce a scatterplot showing the item number and the z-score. (Basically, your scatterplot should let a reader easily tell how many values are within 1 standard deviation of the mean, how many are within 2 standard deviations, etc.)

Day #40:

"A fool must every now and then be right, by chance."


Class time devoted to working on problems using the standard normal distribution curve. (Handout in class.)