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Statistics

Understand the types of data and levels of measurement in statistics. Learn to differentiate between qualitative and quantitative data, and determine the appropriate classification for different data sets.

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Statistics

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  1. Statistics Section 1.2 Data Classification

  2. Types of Data Qualitative Data Attributes Labels Non-numerical observations Examples: Sex, Social Security numbers, uniform numbers on athletic uniforms

  3. Types of Data Quantitative Data Numerical measurement or count Examples: Price of a vehicle, population, age, height, weight, number of siblings

  4. Example Set No.1 Determine whether the following data are qualitative or quantitative. (a) Monthly salaries of the employees of a local bank. Answer: quantitative since salaries are numerical measures

  5. (b) Social Security numbers of employees on a company’s payroll. Answer: qualitative – these are labels and no meaningful arithmetic calculation can be done with these numbers (c) The ages of 350 residents of nursing homes. Answer: quantitative; age is a numerical measure

  6. (d) Zip codes of the home town of students enrolled at Shumway College. Answer: qualitative; zip codes are numbers that identify a region in the country and are hence treated as labels If data are numbers, they are not necessarily quantitative data. If data are numbers, and these numbers cannot be put into an order that has meaning or significance, then they are likely labels and should be considered as qualitative.

  7. Levels of Measurement Data can be classified based upon what types of mathematical calculations can be performed on the observations in the data set (if any can be done at all).

  8. Levels of Measurement Nominal Level Qualitative data only No mathematical calculations can be performed on the observations Data are categorized using names, labels or qualities

  9. Levels of Measurement Nominal Level Examples Color of eyes Social Security number Zip code/area code Jersey number on athletic uniform Type of rock (igneous, sedimentary, metamorphic)

  10. Levels of Measurement Ordinal Level Qualitative or quantitative data Data can be arranged in order (such as rankings) Differences between observations are not meaningful

  11. Levels of Measurement Ordinal Level Examples Ranking in the NCAA football poll Rolling Stone’s Top 100 rock and roll songs of all time Motion picture rating system Ratings such as “below average,” “average” or “above average” Class standing (freshmen, sophomore, junior, senior)

  12. Levels of Measurement Interval Level Quantitative data only Data can be ordered and differences between observations can be calculated meaningfully (the distance between 40 and 50 is the same as the distance between 60 and 70) Zero does not mean “nothing,” but is representative of a position on a scale (examining the meaning of zero is crucial) Operations such as multiplication and division are not meaningful (is 50 degrees twice as warm as 25 degrees?)

  13. Levels of Measurement Interval Level Examples Temperature a temperature of 0 does not mean that there is no heat present; it is a position on the temperature scale Calendar years (there is no “zero” in this case)

  14. Levels of Measurement Ratio Level Quantitative data only An observation of zero is an inherent zero; that is, zero means “none” Ratio of two data values can be meaningfully calculated

  15. Levels of Measurement Ratio Level Examples Money ($0 means you have nothing; $10 is twice as much as $5 and $20 is twice as much as $10) Number of wins (or losses) by a sports team Number of inches of snow

  16. Levels of Measurement Interval Level or Ratio Level? The meaning of zero is critical in distinguishing between these two levels. If one quantity is twice as large as another, does that necessarily mean that it is twice as big (quantitatively) as the other?

  17. Example Set No.2 Determine the level of measurement of each data set. Use the highest level of measurement that the data set falls into to classify. • Daily high temperatures (in degrees Fahrenheit) for Muncy, Pa. Answer: interval

  18. (b) Size class for automobiles (subcompact, compact, midsize, large) Answer: ordinal; qualitative data can be arranged in a meaningful order (c) Four departments of an automobile dealership (sales, services, parts, body shop) Answer: nominal; qualitative data with no meaningful arrangement/order

  19. (d) Heights (in inches) of players on the Muncy High School basketball team(s) Answer: ratio; a player with a height of 68 inches is twice as tall as a player with height of 34 inches

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