  Assignment 54

 "Whereas at the outset geometry is reported to have concerned itself with the measurement of muddy land, she now handles celestial as well as terrestrial problems. She has extended her domain to the furthest bounds of space." -- (Hodder and Stoughton, The Story of Euclid, 1901) Fibonacci (Leonardo of Pisa, 1170-1250). Fibonacci is known for the sequence that bears his name: 1,1,2,3,5,8,13,21,34,55,89,144,... . This amazing sequence appears in a number of natural and human-made creations. It is less well known that Fibonacci studied under Islamic teachers as a result of being with his merchant father on many trips from Italy to what is now Algiers in North Africa. As he grew older, Fibonacci traveled throughout the Mediterranean area, frequently meeting with mathematicians and scholars. Upon returning to his homeland in 1200, he began to write manuscripts that incorporated and expanded the mathematics he had learned in the Islamic world, which was far superior to the cumbersome Roman numeral arithmetic in use at that time. Fibonacci numbers are very evident in nature. They can be seen in the scales of pine cones, the knobbles of pineapples, the leaves of plants, the family tree of a male bee, and in many other elements of nature. Here's an interesting fact: Fibonacci sighed his works with the name "Blockhead." Some research can uncover why he did this. What did Herkimer's girl friend, Edith, say when she learned he had been dating Kate? Answer: "He can't have his Kate and Edith too." Herky's friends: BARB BELL...she was a talented weight lifter. SUE PREME...this girl did everything extremely well. ASSIGNMENT #54 Reading: Section 7.7, pages 445-448. Written: Page 451. Put the data for problems 40-42 into your calculator. Put the ages of the 42 Presidents in L1 and the ages of the 47 Vice Presidents in L2. Use your calculator to produce a box-and-whisker plot for both sets, and a histogram for both sets. Come to some conclusion about the data sets. (Basically, you are doing problems 40,41, and 42.) Mathematical word analysis:SEQUENCE: From the Latin root sequi, which means "to follow." In a mathematical sequence, one number follows another.
Data displays are important in statistics. If you have a lot of data, a box-and-whisker plot can provides lots of information about the data. Terminology is important.

Mean: This is what we normally call the average. Add up the numbers and divide by the number of numbers.

Median: The 50th percentile. Half of the scores are equal to or above this number, and half the scores are equal to or less than this number.

Mode: The most frequently obtained score. (A data set can have more than one mode.)

Lower quartile (25th percentile): One quarter of the numbers are equal to or less than this score.

Upper quartile (75th percentile): Three quarters of the numbers are equal to or less than this score.

Range: Maximum score - minimum score.

Interquartile range: 75th percentile - 25th percentile.

Standard deviation: A measure of spread. (This will be the subject of the next assignment.)

Your TI-83 can produce lots of excellent data displays with numbers provided in the LISTS.

 Problem: Find the mean, median, mode, and range for the data set {60,63,66,72,72,75,80,81,81,91,91,91,100} Solution (with communication):The numbers are in ascending order, making it relatively easy to identify the median, mode, and range. The sum of the numbers is 1,023. Mean = 1,023/13 = 78.69.Median = 80.Mode = 91.Range = 100 - 60 = 40. Problem: Consider the sets S = {94,95,96,97,98}, andT = {14,95,96,97,98}. Compare the means, medians, and ranges of the two sets. Solution (with communication): Both sets have a median of 96. Range of S = 98 - 94 = 4.Range of T = 98 - 14 = 84. Mean of S = 480/5 = 96.Mean of T = 400/5 = 80. Note: One extremely high or low score in a set has a tremendous effect on the mean and range, but not on the median.