Elementary Statistics Picturing the World Data Classification

1.2 Data Types and Levels of Measurements Qualitative data – consist of values that describe qualities or non-numerical (i.e. brand names, letter grades, area codes, social security numbers, gender) Quantitative data – consist of values representing counts or measurements with which you can make meaningful calculations (i.e. IQ scores, percentage grades, price of cars)

1.2 Data Types and Levels of Measurements Four Levels of Measurement: Nominal – data consisting of names, labels, or categories only. The data are qualitative and can not be ranked or ordered Ordinal – qualitative or quantitative data that can be arranged in some order. It generally does not make sense to do computations with ordinal data. Interval – quantitative data which intervals are meaningful, but ratios are not. Data at this level have an arbitrary zero point. Ratio – quantitative data which both intervals and ratios are meaningful. Data at this level have a true zero point.

1.2 Data Types and Levels of Measurements Four Levels of Measurement: Nominal – Flavors, gender, type of car you drive, occupation, social security numbers Ordinal – Movie ratings ( 3 stars vs. 2 stars), BCS College Football Rankings, the order of runners finishing a race Interval – temperature (55 degrees is more than 11 degrees, but 55 degrees is not necessarily 5 times hotter than 11 degrees because 0 does not represent no temperature) Ratio – distances (10 miles is twice 5 miles, and 0 miles means no distance), salary, age

1.2 Data Types and Levels of Measurements

1.2 Data Types and Levels of Measurements Eye color on a dating survey? Qualitative Quantitative

1.2 Data Types and Levels of Measurements Scores on a multiple choice exam? Qualitative Quantitative

1.2 Data Types and Levels of Measurements Flavors of ice cream? Qualitative Quantitative

1.2 Data Types and Levels of Measurements College majors? Qualitative Quantitative

1.2 Data Types and Levels of Measurements Weights of trucks? Qualitative Quantitative

1.2 Data Types and Levels of Measurements Incomes of college graduates? Qualitative Quantitative

1.2 Data Types and Levels of Measurements The numbers on the shirts of a girl’s soccer team? Qualitative Quantitative

1.2 Data Types and Levels of Measurements Student rankings of cafeteria food: excellent, good, fair, poor? Nominal Ordinal Interval Ratio definite order

1.2 Data Types and Levels of Measurements Weights of wrestlers? Nominal Ordinal Interval Ratio true zero point

1.2 Data Types and Levels of Measurements Calendar years of historic events, such as 1776, 1945, 2001? Nominal Ordinal Interval Ratio because dates have no meaningful ratios and zero does not represent beginning of time

1.2 Data Types and Levels of Measurements Numbers on uniforms? Nominal Ordinal Interval Ratio no ordering

1.2 Data Types and Levels of Measurements Temperatures on the Celsius scale? Nominal Ordinal Interval Ratio because temperature has no meaningful ratios and zero degrees does not mean “no heat”

1.2 Data Types and Levels of Measurements Runner’s times in the Boston Marathon? Nominal Ordinal Interval Ratio true zero point

1.2 Data Types and Levels of Measurements Data that can be classified according to color? Nominal Ordinal Interval Ratio

1.2 Data Types and Levels of Measurements The final grades (A, B, C, D, and F) for students in a Probability & Statistics course? Nominal Ordinal Interval Ratio

1.2 Data Types and Levels of Measurements A list of Zip Codes? Nominal Ordinal Interval Ratio

1.2 Data Types and Levels of Measurements The daily temperatures (in degrees Fahrenheit) on five randomly selected days are 22, 21, 31, 36, 21? Nominal Ordinal Interval Ratio

1.2 Data Types and Levels of Measurements Social Security Numbers? Nominal Ordinal Interval Ratio