Statistics The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.
Example of Statistics The 10 most admired companies from a survey of 4000 senior executives Rank Company 1 2 3 4 5 6 7 8 9 10 General Electric Cisco Systems Wal-Mart Stores Southwest Airlines Microsoft Home Depot Berkshire Hathaway Charles Schwab Intel Dell Computer Corp.
Types of Statistics 1. Descriptive statistics Organizing, summarizing and presenting data in an informative way • Graphically • or • -as averages
Graphically: Price $6 $5 $4 $3 $2 $1 0 10 20 30 40 60 50 Number Sold
Averages -The 2001 Honda Odyssey minivan averages 18 miles per gallon in city driving an 25 mpg highway driving • The average credit card debt for people who petitioned the US Bankruptcy Court on March 27, 2001 in Toledo, Ohio was $14,366 and the average medical debt was $8,086. - According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2001. The statistic 9 describes the number of problems out of every 100 machines.
Types of Statistics 2. Inferential statistics The methods used to find out about a population based on a sample Population- all possible individuals, objects, or measurements of interest Sample- a portion of the population
Types of Statistics(examples of inferential statistics) • EXAMPLE 1:TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers. • EXAMPLE 2:The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company. • EXAMPLE 3:Wine tasters sip a few drops of wine to make a decision with respect to all the wine waiting to be released for sale.
For each of the following, determine whether the group is a population or a sample. • The participants in a study of a new diabetes drug 2. The drivers who received a speeding ticket in Kansas City last month 3. Those on welfare in Cook County, Illinois. 4. The 30 stocks reported as part of the Dow Jones Industrial Average.
Variables 1. Qualitative Non-numeric Gender, major, home town 2. Quantitative Reported numerically Test scores, ages, class enrollment
Classify each of the following as qualitative or quantitative: • The weight of each member of a football team. 2. The month of birth of students. 3. Students’ scores on the 1st Statistics exam. 4. The Olympic track and field records. 5. The color of cars in the parking lot.
Types of Quantitative Variables 1. Discrete Usually a gap between values number of family members, student enrollment, cars in the parking lot 2. Continuous Any value within a range amount of snow in Lynchburg last winter, a person’s weight, tire pressure
Classify each of the following as continuous or discrete: • The number of sit-ups 2. The acceleration of an automobile. 3. The number of pairs of shoes sold. 4. The temperature of this room. 5. The diving depth of a submarine.
4 Levels of Measurement 1. Nominal level • data is sorted into classes with no particular order • often non-numeric c.Mutually exclusive – only one category - colors of M&Ms, cars d. exhaustive - each must appear in a category
2. Ordinal level a. data is ranked ( one category is higher than another) - what could you be doing right now? b.Mutually exclusive c. exhaustive • EXAMPLE: During a taste test of 4 soft drinks, Mountain Dew was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4. • mutually exclusive – each is only in one category • exhaustive – each has to be in one of the 4
3. Interval level a. data is ranked and the difference between values is a constant size. - temperatures the last 3 days (zero degrees is no different than 95 degrees) - test scores b. Mutually exclusive – only 1 category or value c. exhaustive – each value must be in a category
4. Ratio level • a meaningful zero point • the ratio of two values is meaningful weight, height and money $20 vs $10 vs $0
Text, page 12 Levels of Data Nominal Data Ordinal Data Interval Data Ratio Data Data may only be classified Data is ranked Meaningful difference between values Meaningful 0 point and ratio between values Hair color, Zip code Order of finish, class temp, test score Income, Distance to class
What is the level of measurement for each of the following variables? • Student IQ ratings. 2. Distance students travel to class 3. Student scores on a statistics test 4. A classification of students by state of birth 5. A ranking of students by freshman, sophomore, junior, or senior 6. Number of hours students study per week.
What is the level of measurement for these items related to the newspaper business? • The number of papers sold each Sunday during 1998. 2. The number of employees in each of the departments, such as editorial, advertising, sports 3. A summary of the number of papers sold by county. 4. The number of years with the paper for each employee