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Mathematical Indices

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

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Mathematical Indices

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

  2. 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)

  3. 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 http://nhlbisupport.com/bmi/bmicalc.htm Underweight Below 18.5 Normal 18.5 - 24.9 Overweight 25.0 - 29.9 Obese 30.0 and Above NOTE: BMI is not accurate for athletes and the elderly

  4. 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

  5. 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 – (35 + 3 + 54) • = 56

  6. Slugging Percentage Example cont’d SLG = (1B + 2×2B + 3×3B+ 4×HR) / AB = (56 + 2×35 + 3×3 + 4×54) / 569 = 351 / 569 = 0.617 • This means Jose attained 0.617 bases per AB

  7. 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 5th 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 http://ca.finance.yahoo.com • Click Charts  Interactive • TECHNICAL INDICATORS  SMA • Useful for showing long term trends

  8. 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. http://www.statcan.gc.ca/cgi-bin/imdb/p2SV.pl?Function=getSurvey&SDDS=2301&lang=en&db=imdb&adm=8&dis=2

  9. 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).

  10. 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.

  11. 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 $1CAD=$.932418 USD.

  12. MSIP / Homework • Read pp. 189-192 • Complete pp. 193-195 #1a (odd), 2-3 ac, 4 (alt: calculate SLG for 3 players on your favourite team for 2010), 8, 9, 11

  13. References • Halls, S. (2004). Body Mass Index Calculator. Retrieved October 12, 2004 from http://www.halls.md/body-mass-index/av.htm • Wikipedia (2004). Online Encyclopedia. Retrieved September 1, 2004 from http://en.wikipedia.org/wiki/Main_Page

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