Mathematical Indices Chapter 3.6 – Tools for Analyzing Data Mathematics of Data Management (Nelson) MDM 4U

What is an Index? An arbitrarily defined number that provides a measure of scale Used to indicate a value so that we can make comparisons, but does not always represent an actual measurement or quantity Interval Data (no meaningful starting point)

1) BMI – Body Mass Index A mathematical formula created to determine whether a person’s mass puts them at risk for health problems BMI =where m = mass in kg, h = height in m Standard / Metric BMI Calculator UnderweightBelow 18.5 Normal Overweight Obese30.0 and Above NOTE: BMI is not accurate for athletes and the elderly

2) Slugging Percentage Baseball is the most statistically analyzed sport in the world A number of indices are used to measure the value of a player Batting Average (AVG) measures a player’s ability to get on base (hits / at bats)  probability Slugging percentage (SLG) also takes into account the number of bases that a player earns (total bases / at bats) SLG = where TB = 1B + 2B × 2 + 3B × 3 + HR × 4, OR TB = H + 2B + 3B ×2 + HR ×3 where 1B = singles, 2B = doubles, 3B = triples, HR = homeruns

Slugging Percentage Example e.g. 3B/OF Jose Bautista, Toronto Blue Jays 2010 Statistics: 569 AB, 148 H, 35 2B, 3 3B, 54 HR NOTE: H (Hits) includes 1B as well as 2B, 3B and HR So  1B = H – (2B + 3B + HR)  = 148 – ( )  = 56

Slugging Percentage Example cont’d SLG = (1B + 2×2B + 3×3B+ 4×HR) / AB = (56 + 2×35 + 3×3 + 4×54) / 569 = 351 / 569 = This means Jose attained bases per AB

Example 3: Moving Average Used when time-series data show a great deal of fluctuation (e.g. stocks, currency exchange) Average of the previous n values e.g. 5-Day Moving Average  cannot calculate until the 5 th day  value for Day 5 is the average of Days 1-5  value for Day 6 is the average of Days 2-6 e.g. Look up a stock symbol at Click Charts  Interactive TECHNICAL INDICATORS  SMA Useful for showing long term trends

Other Examples 1) Consumer Price Index (CPI)  An indicator of changes in Canadian consumer prices  Compares the cost of a fixed basket of commodities through time  Commodities are of unchanging or equivalent quantity and quality reflecting only pure price change. bin/imdb/p2SV.pl?Function=getSurvey&SDDS=2301&lang =en&db=imdb&adm=8&dis=2

What is included in the CPI? 8 major categories  FOOD AND BEVERAGES (breakfast cereal, milk, coffee, chicken, wine, full service meals, snacks)  HOUSING (rent of primary residence, owners' equivalent rent, fuel oil, bedroom furniture)  APPAREL (men's shirts and sweaters, women's dresses, jewelry)  TRANSPORTATION (new vehicles, airline fares, gasoline, motor vehicle insurance)  MEDICAL CARE (prescription drugs and medical supplies, physicians' services, eyeglasses and eye care, hospital services)  RECREATION (televisions, toys, pets and pet products, sports equipment, admissions);  EDUCATION AND COMMUNICATION (college tuition, postage, telephone services, computer software and accessories);  OTHER GOODS AND SERVICES (tobacco and smoking products, haircuts and other personal services, funeral expenses).

Other Examples cont’d 2) NHL Fan Cost Index (FCI) Comprises the prices of:  four (4) average-price tickets  two (2) small draft beers  four (4) small soft drinks  four (4) regular-size hot dogs  parking for one (1) car  two (2) game programs  two (2) least-expensive, adult-size adjustable caps.

Other Examples cont’d 2) NHL Fan Cost Index (FCI) Details Average ticket price represents a weighted average of season ticket prices. Costs were determined by telephone calls with representatives of the teams, venues and concessionaires. Identical questions were asked in all interviews. All prices are converted to USD at the exchange rate of $1CAD=$ USD.

MSIP / Homework Read pp Complete pp #1a (odd), 2-3 ac, 4 (alt: calculate SLG for 3 players on your favourite team for 2010), 8, 9, 11

References Halls, S. (2004). Body Mass Index Calculator. Retrieved October 12, 2004 from Wikipedia (2004). Online Encyclopedia. Retrieved September 1, 2004 from