Section 1-3 Types of Data

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

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

Tips to Know Whether you have a Parameter or Statistic: Ask yourself, is this a fact about the whole population? Sometimes that’s easy to figure out. For example, with small populations, you usually have a parameter because the groups are small enough to measure. Examples: 10% of US senators voted for a particular measure. Since there are only 100 US Senators, it is possible to see how every single senator voted. 40% of 1,211 students at a particular elementary school got below a 3 on a standardized test. Again, this is a relatively small population so you could have each and every students’ test score. 33% of 120 workers at a particular bike factory were paid less than $20,000 per year. Again, 120 workers is a small population so it is possible to know how much each worker was paid.

More Tips… Ask yourself, is this obviously a fact about a very large population? Perhaps so large that a sample is necessary? If it is, you have a statistic. Examples: 60% of US residents agree with the latest health care proposal. It’s not possible to actually ask hundreds of millions of people whether they agree. Instead, we would take a sample of the entire population of US residents. 45% of Jacksonville, Florida residents report that they have been to at least one Jaguars game. Again, we have a large population of people (over 1 million) so a sample of all Jacksonville residents would be asked. 30% of dog owners clean up (poop scoop) after their dog. It’s impossible to survey all dog owners—no one keeps an accurate track of exactly how many people own dogs. This data had to be from a sample, so it’s a statistic.

Example 1: 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 2: 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 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 (Also a voluntary response sample).

Examples: 3) 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 4.) 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

Examples: 5.) 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 6.) 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 volts. Statistic

Quantitative Data Quantitative (or numerical) data consists of numbers representing counts or measurements. Example: The heights 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 names on professional athletes uniforms.

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 days in a school year, the number of kittens in a litter, etc.

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: Height, age, weight, time, temperature (measurements)

Example 7: 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 8: 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 9: 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 and IVF Institute, 726 couples used the XSORT method and 668 of them had baby girls. Discrete

Example 10: 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.

Brain Break Halitosis is the medical term for what? Who won Superbowl 1? Where do the Griffins from Family Guy live?

Nominal Level Nominal level of measurement characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in order (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 Temperatures keep going past zero

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 (words not numbers) Ordinal - categories with some order (numbers are possible, but only if in context of categories) Interval - differences but no natural starting point (think years, temperatures, etc.) Ratio - differences and a natural starting point (zero is possible and would make sense) Table 1.2 on page 15 of your textbook is a great summary as well.

Example 11: 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 – zero is possible and could make sense

Example 12: 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 – there is clear ordering with 4 stars being better than 3, and 3 stars better than 2, etc. **Note – Numbers are typically used for ordinal data. If they are used, it’s in context of a clear order and each number represents a clear category. In this example, “0 star” represents a category not a specific number.

Example 13: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: Companies (Disney, MGM, Warner Brothers, Universal, 20 th Century Fox) that produced the movies listed in Data Set 7 in Appendix B in your textbook. Nominal – words/categories

Example 14: 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 – No natural starting point (you wouldn’t begin a zero).