Agenda Introduction to Statistics Descriptive Statistics Measures of Center Measures of Spread - Variability

Statistics Descriptive Statistics Statistics to summarize and describe the data we collected Inferential Statistics Statistics to make inferences from samples to the populations

Descriptive Statistics

A summary of your data 1.Measures of Center 2.Measures of Spread 3.Measures of Association ( Shown in Tables, Graphs, Distributions )

Distribution: Gender BoyGirl (n=15) Gender Number of Kids

Statistics How can you explain your data without showing the whole thing? Descriptive Statistics

Example: Mode GENDER Boys: 40%Girls: 60%

Central Tendency CENTER The most typical value for the variable A single value that best represents the variable

Measures of Center Indicates a central value for the variable Mode Median Mean

Mode the most common value Measure of centerfor nominal variables A value with the highest frequency A variable can have more than one mode

Example: Mode ENTREE Meat: 35%Fish: 30%Veggie: 35% Bimodal

Median A measure of center for ordinal variables The “middle” score The value the middle case falls in When the sample has an even number and there is no one middle score, take the mean of two middle scores

Example: Median Course Grade A =5 B =7 C =5 D =2 N = 19 Where is the 10 th person?

Distribution: Distance CloseMediumFar Distance Number of Kids (n=15) Very Far Very Close

Distance: Median Median Very Close CloseMed Very Far FarMed

Logic of Median “Middle” Score Median is central because it is the balancing point of the number of cases

Distribution: Age AGE Number of Kids (n=15)

Age: Median

Mean A measure of center for interval/ratio variables “Average” Mean = (Sum of scores) / Sample size Presented as

MEAN  Formula:  = sum, add up X = each person’s score / = divide by N = # of people

WHY are LEVELS of MEASUREMENT IMPORTANT? Because you need to match the statistic you use to the kind of scale you use to measure a variable

Measures of Central Tendency NominalOrdinalInterval/Ratio Mode Median Mean

Example: Mean Weight (n=5) 170 lb.Mean 850 lb.Sum 250 lb.#5 200 lb.#4 150 lb.#3 150 lb.#2 100 lb.#1

Lesson Descriptive statistics help you understand data for each variable Know level of measurement of your variables Match the statistic to the scale used to measure variable

Fall 2002

TASK 2: Compute central tendencies 5,000BS +Grad student10 20,000MSCounselor9 20,000BSDHS worker8 15,000BSA+ director7 0BSHome-maker6 0BSUnemployed5 0BSUnemployed4 25,000BS +DOE teacher3 15,000MSChild care2 10,000BSChild care1 SALARYEDUCATION EMPLOYMENT PERSON

What happens to mean salary if we add 11 th grad who earns $500,000? 500,000BSDay trader11 5,000BS +Grad student10 20,000MSCounselor9 20,000BSDHS worker8 15,000BSA+ director7 0BSHome-maker6 0BSUnemployed5 0BSUnemployed4 25,000BS +DOE teacher3 15,000MSChild care2 10,000BSChild care1 SALARYEDUCATION EMPLOYMENT PERSON

What are the Mean, Median, and Mode for this distribution? What is this distribution shape called?