Statistics Data

Other Variables Alaska Airlines 501/3775 = 13.3% On Time Delayed Alaska Airlines 3274 501 America West 6438 787 Alaska Airlines 501/3775 = 13.3% America West 787/7225 = 10.9% Alaska Airline America West On Time Delayed Los Angeles 497 62 694 117 Phoenix 221 12 4840 415 San Diego 212 20 383 65 San Francisco 503 102 320 129 Seattle 1841 305 201 61 Total 3274 501 6438 787 Los Angeles: Alaska Airline 62/559 = 11.1% America West 117/811 = 14.4% Phoenix: Alaska Airline 12/233 = 5.2% America West 415/5255 = 7.9%

“70% OF PARENTS SAY KIDS NOT WORTH IT” Quote from Ann Landers article A statistically designed poll where all parents get an equal chance to answer shows 91% of parents would have children again. A new advertisement for Ben and Jerry’s ice cream introduced in late May of last year resulted in a 30% increase in ice cream sales for the following three months. Thus, the advertisement was effective. The more churches in a city, the more crime there is. Thus, churches lead to crime.

Statistics Has become more popular over the past 4 decades or so. Why?? Computers and computer software! Used for research in nearly every possible profession. A lot of college programs require some type of statistics class.

True or False “There are three kind of lies: lies, damned lies, and statistics.” However, statistics are numerical facts such as: Family income Age of a student Percentage of passes completed Starting salary of a college graduate

Definition Statistics – a group of methods used to collect, analyze, present, and interpret data and to make decisions Make an educated guess (statistics) vs a pure guess (a shot in the dark). Think about multiple choice questions.

Theoretical vs applied Theoretical (or mathematical) statistics – development, derivation, and proof of statistical theorems, formulas, rules, and laws Applied – application of those theorems, formulas, rules, and laws We will focus on applied so we can think statistically and make educated guesses.

More Definitions Using data collected on student test scores as an example Data set elements observation Test scores Test 1 Test 2 Test 3 Test 4 Allen 79 83 70 81 Betty 98 90 92 85 Carl 91 93 Diane 61 75 Variable

Data set – collection of observations or measurements - the whole set of numbers that represents the scores of the students Element (or Member) – a specific subject or object included in a sample or population - name of each student Observation (or Measurement) – the value of a variable for an element - score for each student Variable – a characteristic under study that assumes different values for different elements - each test

Practice 1. 2. Season Average attendance at Interleague Games 1999 33352 2000 33212 2001 33692 2002 31921 2003 30894 2004 32976 Company 2004 Profits (millions of $) Wal-Mart Stores 10267 Exxon 25330 General Electric 16593 Citigroup 17046 Home Depot 5001 Pfizer 11361 Target 3198 Give examples of a variable, an observation or measurement, an element or member, and data set

Descriptive Statistics Data sets are usually too large, so we use Graphs Tables Summary measures Descriptive Statistics – consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures

Inferential Statistics Since it is not easy to get data on entire populations (collection of all elements of interest) we use a sample (selection of a few elements from the population). Inferential Statistics – consists of methods that use sample results to help make decisions or predictions about a population

Population vs. Sample Suppose we are interested in The percentage of all voters in a city who will vote for a particular candidate in an election The 2005 gross sales of all companies in New York City The price of all houses in California In these examples notice ALL voters, ALL companies, and ALL houses

Population vs. Sample Population - consists of all elements – individuals, items, or objects – whose characteristics are being studied Sample – a portion of the population selected for study

Practice Explain whether each of the following constitutes a population or a sample Pounds of bass caught by all participants in a bass fishing derby. Credit card debts of 100 families selected from a city. Number of home runs hit by all Major League baseball players in the 2009 season. Number of parole violations by all 2147 parolees in a city. Amount spent on prescription drugs by 200 senior citizens in a large city. Yearly expenditures on clothes for 50 persons. Total items produced on a machine for each year from 1995 to 2005.

Survey and Census Survey – collection of information from the elements of a population or sample Census – survey that includes every element of the target population Since census is expensive and time consuming we usually use a sample of elements from the whole population A sample survey is a technique of collecting information from a portion of the population

Other samples Representative Sample – sample that represents the characteristics of the population as closely as possible Average income of New York City families Random Sample – a sample draw in such a way that each element of the population has an equally likely chance of being selected.

To replace or not to replace… With replacement – each time we select an element from the population, we put it back in the population before we select the next element. (we can select the same element more than once) Without replacement – the selected element is not replaced back into the population, therefore reducing the population by one element for the next selection. (we cannot select the same element more than once)

Quantitative vs. Qualitative Quantitative variable – A variable that can be measured numerically Discrete variable – a variable whose values are countable, or can only assume certain values with no intermediate values Continuous variable – A variable that can assume any numerical value over a certain interval or intervals Qualitative (or Categorical) variable – A variable that cannot assume a numerical value but can be classified into two or more nonnumeric categories

Quantitative (numerical) Variable Quantitative (numerical) Discrete (number of houses, students, cows in a field) Continuous (height, weight, time) Qualitative (make of car, hair color, gender)

Practice Indicate which of the following variables are quantitative and which are qualitative. Number of persons in a family Color of cars Marital status of people Length of a frogs jump Number of errors in a person’s credit report Number of typographical errors in newspapers Monthly TV cable bills Spring break locations favored by college students Number of cars owned by families Lottery revenues of states

Practice discrete vs. continuous Indicate which of the following quantitative variables are discrete and which are continuous. Number of persons in a family Length of a frogs jump Number of errors in a person’s credit report Number of typographical errors in newspapers Monthly TV cable bills Number of cars owned by families Lottery revenues of states