The Nature of Statistics · 2013-09-24 · day 1 mt4.notebook August 22, 2013 Uses of Statistics: Why is statistics important? Based on the 2000 census, 40.5 million households have

day 1 mt4.notebook August 22, 2013

Please find your seat on the seating chart,

turn in your signed portion of the syllabus to the basket,

and be prepared to get to work.

The Nature of Statistics• Branches of Statistics• Variables and Types of Data• Levels of Measurement• Sampling Methods

mt4


Uses of Statistics: Why is statistics important?Based on the 2000 census, 40.5 million households have 2 vehicles. (source: US Census Bureau)

The average annual salary for an NFL player in 2012 was $1,900,000. (source: Forbes)

The median salary for men with bachelor's degrees is $49,982, while the median salary for women with a bachelor's degree is $35,408. (source: Census Bureau)

Women who eat fish once a week are 29% less likely to develop heart disease. (source: Harvard School of Public Health)

The Wall Street Journal discussed the disappearance of fireflies. It seems the worldwide population is declining.

Reasons for the decline?*reduction of their habitat*pesticides and pollution*artificial nighttime lighting *bounty offered for their chemicals: medical research & electronic detection systems used in spacecraft.

What does this have to do with statistics?

At any given time no one knows how much the firefly population has declined or how to explain the decline. The population is just too large to study in its entirety.

So, we rely on information from samples small groups of fireflies. We draw conclusions from these smaller groups

To do this correctly, we must make sure the sample accurately represents the entire population of fireflies.


Statistics:the science of conducting studies to collect, organize, analyze, and draw conclusions from data.

Why study statistics?To be able to read and understand the various statistical studies performed in their fields. You must know about symbols, terms, and procedures.

You may be called on to do research in your field (nursing, education, business, agriculture, political science, etc.)

To be a better consumer and citizen; to understand what's going on in the world

Individual:the person/object included in a study

students, camels, girls, etc.

Variable:a characteristic of an individual measured or observed (differs)

eye color, height, eating habits, handedness*when the variable is chosen by chance, then it is considered to be a Random Variable.

Data:the values a variable can assume

eye colors: green, blue, brown, etc.heights: 52", 68", 72", etc.


TWO BRANCHES OF STATISTICSData can be used in different ways. There are two main areas in which data can be classified.

1. DESCRIPTIVE STATISTICS

2. INFERENTIAL STATISTICSdescribes situations using categories/labels or numbers

Uses what is known to make predictions or educated guesses

DESCRIPTIVE STATISTICSA situation is described by using different measures or calculations.It is the collection, organization, summarization, and presentation of data.

• Pie Charts• Bar Graphs (histograms)• Time Series Charts• Frequency Polygons• Mean• Median• Mode• Midrange• Range...and many more...


INFERENTIAL STATISTICSUses a small group to make general conclusions about a larger group.Performs estimations, tests hypotheses, and make predictions using probability.

• Hypothesis Testing• Confidence Intervals• Correlation and Regression...and many more...

PRACTICE!Determine if the following represents descriptive (D) or inferential (I) statistics.

1. In the year 2025, 148 million Americans will be enrolled in an HMO.2. Nine out of ten onthejob deaths are men.3. Costs for the cable industry were $5.66 billion in 1996.4. The median household income for people aged 2534 is $35,888.5. Allergy therapy makes bees go away.6. Drinking decaf coffee may raise cholesterol levels by 7%.7. The national average amount of money a person spends on medicine per year is $1052.8. Experts say that mortgage rates will soon hit rock bottom.

Answers: 1. I 2. D 3. D 4. D 5. I 6. I 7. D 8. I


Terminology for Statistics

Population: the entire group to be studied

Sample: a subgroup of the population

POPULATION DATA: data from every person/thing in the study

Parameter: a # measurement from a population

one classroom entire school


SAMPLE DATA: data are from some of the individuals in the study

Statistic: a # measurement from a sample

one classroomentire school

Every student at PVHS = population data The % PVHS students that are male = a

parameter

20 seniors at PVHS = sample data The % males in that group 20

seniors = statistic

For Example...

never cha

nges

varies dep

ending o

n

sample


VARIABLES AND TYPES OF DATAQualitative:variables that can be placed into distinct categories according to some kind of quality or attribute

gender, race, political affiliation, zip code, hair colorQuantitative:variables that are numerical and can be ordered or ranked.

age, heights, body temperatures, # of students in classroom

VARIABLES

Qualitative Quantitative

Discrete Continuous

counted measured


PRACTICE!Qualitative Quantitative (discrete or continuous)

1. colors of cars in a faculty parking lot2. number of desks in a classroom3. classifying children as infant, toddler, or preschool4. weights of fish caught in Lake Hartwell5. number of pages in a statistics book6. capacity (# gallons) of water in the Hoover Dam7. number of offroad vehicles sold in the US last month8. number of loaves of bread baked each day at a local bakery9. water temperature of your shower10. voltage of the battery in your calculator11. number of pizzas sold last year in the US

Answers: 1. Qual 2. Discrete 3. Qual 4. Continous 5. Discrete 6. Continuous7. Discrete 8. Discrete 9. Continous 10. Continous 11. Discrete

LEVELS OF MEASUREMENTNominal:classifies data into mutually exclusive (nonoverlapping) categories in which no order or rank can be imposed on data

zip code, eye color, religion, nationality

Ordinal:classifies data into categories that can be ranked or ordered; but there is no distinguishable difference in the ranks

letter grade, rating scales, rankings of sports athletes/teams

Interval:ranks data; precise differences can be found between the units of measure; but there is no meaningful "zero" (zero ≠ the very bottom)

temperatures, SAT scores, IQ scores

Ratio:possesses all attributes of interval, but has a meaningful zero

*the highest level of measurement*height, weight, salary, age, time


PRACTICE!Determine the level of measurement: nominal, ordinal, interval, ratio.

1. Horsepower of motorcycle engines (350, 400, etc.)2. ratings of newscasts in Houston as poor, fair, good, excellent3. temperatures of automatic popcorn poppers4. time required to brush your teeth5. salaries of teachers6. marital status of police officers (married, single, divorced, widowed)7. ages of students enrolled in a college math course8. weights of beef cattle fed a special diet9. # of pages in the Los Angeles telephone book10. IQ score of statistics instructors at Anderson UniversityAnswers:1. ratio2. ordinal3. interval4. ratio5. ratio6. nominal7. ratio8. ratio9. ratio10. interval

Documents

The Nature of Statistics · 2013-09-24 · day 1 mt4.notebook August 22, 2013 Uses of Statistics: Why is statistics important? Based on the 2000 census, 40.5 million households have