Section 1-3 Types of Data

Parameter population parameter Parameter a numerical measurement describing some characteristic of a population. population parameter

Statistic sample statistic Statistic a numerical measurement describing some characteristic of a sample. sample statistic

Example 1: Determine whether the given value is a statistic or a parameter: In a large sample of households, the median annual income per household for high school graduates is $19,856 (based on data from the U.S. Census Bureau). Statistic

Example 2: Determine whether the given value is a statistic or a parameter: A study of all 2,223 passengers aboard the Titanic found that 706 survived when it sank. Parameter

Example 3: Determine whether the given value is a statistic or a parameter: If the areas of the 50 states are added and the sum is divided by 50, the result is 196,533 square kilometers. Parameter

Example 4: Determine whether the given value is a statistic or a parameter: The author measured the voltage supplied to his home on 40 different days, and the average (mean) value is 123.7 volts. Statistic

Quantitative Data Quantitative (or numerical) data consists of numbers representing counts or measurements. Example: The weights of supermodels. Example: The ages of respondents.

Categorical Data Categorical (or qualitative or attribute) data consists of names or labels (representing categories). Example: The genders (male/female) of professional athletes. Example: Shirt numbers on professional athletes uniforms - substitutes for names.

Working with Quantitative Data Quantitative data can further be described by distinguishing between discrete and continuous types.

Discrete Data Discrete data result when the number of possible values is either a finite number or a ‘countable’ number. (i.e. the number of possible values is 0, 1, 2, 3, . . .) Example: The number of eggs that a hen lays.

Continuous Data Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps.

Example 5: Determine whether the given values are from a discrete or continuous data set: In New York City, there are 3,250 walk buttons that pedestrians can press at traffic intersections, and 2,500 of them do no work (based on data from the article “For Exercise in New York Futility, Push Button, “ by Michael Luo, New York Times). Discrete

Example 6: Determine whether the given values are from a discrete or continuous data set: The amount of nicotine in a Marlboro cigarette is 1.2 mg. Continuous

Example 7: Determine whether the given values are from a discrete or continuous data set: In a test of a method of gender selection developed by the Genetics & IVF Institute, 726 couples used the XSORT method and 668 of them had baby girls. Discrete

Example 8: Determine whether the given values are from a discrete or continuous data set: When a Cadillac STS is randomly selected and weighed, it is found to weigh 1,827.9 kg. Continuous

Levels of Measurement Another way to classify data is to use levels of measurement. Four of these levels are discussed in the following slides.

Nominal Level Nominal level of measurement characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme (such as low to high). Example: Survey responses yes, no, undecided.

Ordinal Level Ordinal level of measurement involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless. Example: Course grades A, B, C, D, or F.

Interval Level Interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful, however, there is no natural zero starting point (where none of the quantity is present). Example: Years 1000, 2000, 1776, and 1492.

Ratio Level Ratio level of measurement the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present); for values at this level, differences and ratios are meaningful. Example: Prices of college textbooks ($0 represents no cost, a $100 book costs twice as much as a $50 book).

Summary - Levels of Measurement Nominal - categories only Ordinal - categories with some order Interval - differences but no natural starting point Ratio - differences and a natural starting point Table 1.2 on page 15 of your textbook is a great summary as well.

Example 9: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: Voltage measurements from the author’s home (listed in Data Set 13 in Appendix B from your textbook.) Ratio

Example 10: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: Critic ratings of movies on a scale from 0 star to 4 stars. Ordinal

Example 11: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: Companies (Disney, MGM, Warner Brothers, Universal, 20th Century Fox) that produced the movies listed in Data Set 7 in Appendix B in your textbook. Nominal

Example 12: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: Years in which movies were released, as listed in Data Set 9 in Appendix B in your textbook. Interval

Example 13: Identify the (a) sample and (b) population. Also, determine whether the sample is likely to be representative of the population: The newspaper USA Today published a health survey, and some readers completed the survey and returned it. Sample: The readers who returned the completed survey. Population: all readers of USA Today (answers may vary). The sample is not likely to be representative of the population because it is a voluntary response sample.

Example 14: Identify the (a) sample and (b) population. Also, determine whether the sample is likely to be representative of the population: Some people responded to this request: “Dial 1-900-PRO-Life to participate in a telephone poll on abortion. ($1.95 per minute. Average call 2 minutes. You must be 18 years old.)” Sample: The people who responded. Population: The population presumably consisted of all adults at least 18 years of age. The sample is not likely to be representative of the population because those with strong opinions about abortion are more likely to respond.