Section 1.1 Handout
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Mathematics
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Jun 26, 2024
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Math 1342
Dr. Tarcia Hubert
Name: ___Eytravia Franklin______
Section 1.1 – Introduction to the Practice of Statistics
“Nothing is impossible. The word itself says I’m possible!” ~Audrey Hepburn
Video 1: Introduction to Statistics
What is statistics?
Statistics is the science of collecting, organizing, summarizing, and analizing data to answer questions. Example:
A community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks how many hours per week each works. The average number of hours the 128 students worked was 25 hours.
Key Terms: Data: The information collected; Information used to describe the charachteristics of an individual.
Ex: Amount of hours per week each student worked
Population: The entire group of individuals to be studied
Ex: Full time students
Individual: A member or object of the population being studied
Ex: Full-time students
Sample: A subset of the population being studied
Ex: 128 students
Math 1342
Dr. Tarcia Hubert
Name: ___Eytravia Franklin______
Statistic: A numerical summary based on a sample
Ex: 25 hours
Inferential Statistic: Uses methods that take results from a sample, extends them to the population, and measures the reliability of the results.
Descriptive Statistic: Consists of organizing and summarizing data
Typically uses numerical summaries, tables, and graphs to describe the data.
Parameter: A numerical summary of a population
Ex: Ask full-time students how many hours they work a week and then take the average of these hours. The average number of hours would be the parameter.
Example 1: Determine whether the underlined value is a parameter or statistic?
a)
The average score for a class of 30 students taking a final exam was 75%
. Parameter
b)
13.5%
of Americans age 12 and over used drugs in the last month.
Statistic
Video 2: Quantitative vs. Qualitative Data
Variables: The characteristics of the individuals within the population
Variables change !
Qualitative Variables: Aka categorical variables
Allow for classification of individuals based on some attribute
or characteristic.
Ex: Educational level, gender, marital status, name, id number, etc.
Math 1342
Dr. Tarcia Hubert
Name: ___Eytravia Franklin______
Quantitative Variables: Provide numerical measures of individuals.
Values can be added or subtracted and provide meaningful results.
Ex: GPA, bank account balance, salaries, # of followers, etc.
Example 1: Determine whether the following variables are qualitative or quantitative?
a)
Gender
Qualitative
b)
Temperature
Quantitative
c)
Number of days a student studied
Quantitative
d)
Zip code
Qualitative
Discrete vs Continuous Variables
Discrete Variables
: A quantitative variable that has either a finite number of possible values
or a countable number of possible values. If you count to get the value of a quantitative variable, then it’s discrete.
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Math 1342
Dr. Tarcia Hubert
Name: ___Eytravia Franklin______
Continuous Variables
: A quantitative variable that has an infinite number of possible values.
If you measure to get the value of a quantitative variable, then its continuous.
Example 2: Determine whether the quantitative variables are discrete or continuous.
a)
The number of tails obtained after flipping a coin four times.
Discrete
b)
The number of cars that arrive at a Wendy’s drive through between 9 PM and 10 PM.
Discrete
c)
The distance a 2024 Honda Civic can travel in city conditions with a full tank of gas.
Continuous Video 3: Level of Measurement of a Variable
Nominal Level: A variable is at the nominal level if the variable name, label, or categorize
Ex: Blood type & Eye color
Math 1342
Dr. Tarcia Hubert
Name: ___Eytravia Franklin______
Ordinal Level: A variable is at the ordinal level if the variable has the properties of the nominal level of measurement, and the names allow for the value of the variables to be arranged in a ranked or specific order.
Ex: Socio-economic status (low class, middle class, high class) & satisfaction ratings (extremely dislike, dislike, neutral, like, extremely like)
Interval Level: A variable that has the properties of the ordinal level of measurement, and the differences of the values of the variable have meaning.
A value of zero doesn’t mean an absence of the quantity.
Ex: Temperatures & Credit scores
Ratio Level: A variable that has the properties of the interval level of measurement, and the ratios of the values of the variable have meaning.
A value of zero means an absence of the quantity.
Ex: Money & Weight
Math 1342
Dr. Tarcia Hubert
Name: ___Eytravia Franklin______
Example 1: Determine the level of measurement for each of the following variables.
a)
Gender
Nominal
b)
SAT score
Interval
c)
Number of days a student worked out last week
Ratio
d)
Letter grade
Ordinal
Qualitative
Nominal
Ordinal
Quantitativ
e
Interval
Ratio
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