What is Statistics?Why Study Statistics?

Key Concepts of Statistics

Introducing the Basic Words of the Survey

Introduction to Statistics 2

What is the Discipline of Statistics?

• The art and science of collecting, analyzing, presenting, interpreting and distilling data

• Applied mathematics, different from all other math courses you’ve ever taken

• It’s ‘chatty’math, imprecise and subject to interpretation.

• Statistics is about common sense

Stats as a Discipline

Type of Mathematics

How different?

Most important element?

Introduction to Statistics 3

2 Dictionary Meanings for the Word ‘Statistics’

1. A set of numerical facts

2 The method used to collect, analyze, present, interpret and distill data to make intelligent decisions

Introduction to Statistics 4

How Can Statistics Help Us?

Stats help us make scientific

and intelligent decisions,

often called educated guesses about real

life phenomena

Introduction to Statistics 5

What happens without Statistics?

Without stats we live in

uncertainty with no

precise solutions to real-life problems.

Introduction to Statistics 6

Key Vocabulary in Surveys

• _______Statistical surveys usually begin with a general idea we want an answer for

• _______The entire collection of individuals or objects about which information is desired

• _______A subset of the populationselected for a study by some specific criteria or in a prescribed manner. Usually chosen randomly.

Introduction to Statistics 7

Key Vocabulary Continued• ________ A study using the entire

population• ________ An object which is one

member of the sample. The member could be a person, animal or thing

• ________ Any characteristic of an individual. These characteristics take on different values for different individuals.

Introduction to Statistics 8

Key Vocabulary Continued

• _______ A voluntary encounter between strangers, one the interviewer and the other the individual.

• _______ A person who seeks information from the individual by engaging in a special type of conversation.

• ________ Numbers collected in a particular context. During a survey, the interviewer collects this. Almost always has units.

• ________ The person who analyzes, distillsand interprets the data collected.

Introduction to Statistics 9

Key Vocabulary Continued

• _________Take the data. Crunch it. Interpret it in context.

• _________Take the conclusions and decide if they apply to the sample only or to the larger population.

Introduction to Statistics 10

Key Vocabulary Continued

• Here are three terms: Individual, Sample and Population. Generally speaking, in set theory terms, for a survey,individual sample population

If however, all individuals = sample = population,

then you have a census.

Individual

Sample

Population

Individual

Sample = Population

Normal Survey

Census

Individual

All Individuals=

Introduction to Statistics 11

Good Data vs. Bad Data

Good Data The result of intelligent

effort and good random sampling methods

Bad Data The result of laziness, lack

of understanding, bad sampling technique or the desire to mislead others

Introduction to Statistics 12

Applying Statistical Vocabulary--Example

• Question Is achievement at Washington High School different for males vs. females?

• Survey We want to know if Washington HS gender population has different achievement, so we design a survey to answer the question.

Why gather the data?

Introduction to Statistics 13

Applying Statistical Vocabulary—Cont’d• Population Begin by using

WHS as our population to study• Pop vs. Sample Do we have to use the

whole population of WHS or can we sample them?

• Sample Size If a sample, then how many individuals should we choose & how should we choose them? We decide on 200 students, 100 males and 100 females, 50 from each of the freshmen,

sophomores, juniors and seniors.• How to Sample? We will RANDOMLY choose

individuals in each category

Introduction to Statistics 14

Applying Statistical Vocabulary—Cont’d

• Individuals Randomly select 25-25-25-25 males by class and 25-25-25-25females by class in the school

• Variable What data will we collect?Decide on “What is your GPA?”--as a measure of achievement

• Data Collect it by interview or by looking at ‘office data.’ Collect GPA numbers for our 4 levels of males vs. 4 levels of females.

• Units of Data The unit of GPA is a number between zero and four in points.

Introduction to Statistics 15

Applying Statistical Vocabulary—Cont’d

• Analysis Compare the ‘average’ GPA’s for males vs. females for each grade level at WHS, using our collected data. Compare overall GPA’s, too.

• Conclusion 1) GPA’s are the similar for

Possibilities males and females

2) GPA’s are higher for males vs. females;

3) GPA’s are higher for females vs. males

• Applicability Are our conclusions true for the entire population of WHS? Or for all American high school students?

Introduction to Statistics 16

Elements of a Survey

1 What question is to be answered?

2 Why specifically are we gathering the data? (What do we want to know?)

3 What population is going to be used to answer the question?

4 What sample of the population represents the whole?

5 How is the sample chosen?

6 Is the sample random?

Introduction to Statistics 17

Elements of a Survey

7 How many individuals in the sample are chosen and in what units?

8 What is the variable to be measured and what data represents that variable?

9 What are the units for each piece of data collected?

10 Any question about the trustworthiness of the data?

Introduction to Statistics 18

Elements of a Survey

11 What are some general conclusions to be drawn about the results?

12 Can we apply the conclusions to the entire population? Can we apply the conclusion beyond the population?

Introduction to Statistics 19

CW 100—Fast Food & USA

Today

1 What question was trying to be answered? (by implication)

2 Why specifically were the data gathered?

3 What population was the focus? (by implication)

4 Was the survey a census or a sample?

5 How do you know your answer to #4 is correct? (full sentence)

6 Describe the sample: including units, numbers, conditions.

7 How were the individuals chosen? Was the sample random?

8 What was the variable? (What characteristic was measured?)

9 What were the units of the variable?

10 Any question about the trustworthiness of the data? Describe ina full sentence.

11 Who analyzed the data?

12 What are at least 2 conclusions YOU can draw from the results?(full sentences)

A

B13 Can you apply these conclusions to the whole population? Why

or why not? (full sentence)

Introduction to Statistics 20

Key Vocabulary in Statistics--Answers

• Question Statistical surveys usually begin with a general idea we want an answer for

• Population The entire collection of individuals or objects about which information is desired

• Sample A subset of the populationselected for a study by some specific criteria or in a

prescribed manner

Introduction to Statistics 21

Key Vocabulary Continued--Answers• Census A study using the entire

population• Individual An object which is one

member of the sample. The member could be a person, animal or thing

• Variable Any characteristic of an individual. These

characteristics take on different values for different individuals.

Introduction to Statistics 22

Key Vocabulary Continued--Answers

• Survey A voluntary encounter between strangers, one the interviewer and the other the individual.

• Interviewer A person who seeks information from the respondent by engaging in a special type of conversation.

• Data Numbers collected in a particular context. During a survey, the interviewer collects this. Always has units.

• Statistician The person who analyzes, distillsand interprets the data collected.

Introduction to Statistics 23

Key Vocabulary Continued--Answers

• Analysis Take the data. Crunch it. Interpret it in context.

• Applicability Take the conclusions and decide if they apply to the sample only or to the larger population.

Introduction to Statistics 24

The 4-Tardy Rule

DON’T BE TARDY TO CLASS!• On your 3rd tardy to class during a semester I will

remind you that you have reached my limit.• On your 4th tardy to class, I will deduct 2 points

from your next test.• On each succeeding tardy after that, you will

also lose another 2 points.• Lost points can make a HUGE difference in your

grade. . .