STA 2023

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# STA 2023 - PowerPoint PPT Presentation

STA 2023. Chapter 1 Notes. Terminology. Data: consists of information coming from observations, counts, measurements, or responses. Statistics: the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.

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### STA 2023

Chapter 1 Notes

Terminology
• Data: consists of information coming from observations, counts, measurements, or responses.
• Statistics: the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.
• Population: the collection of all data of interest.
• Sample: a subset, or part, of a population.
EXAMPLE 1: Identify the population and sample.
• A survey of 1353 American households found that 18% of the households own a computer.
• Population: All American households
• Sample: The 1353 American households that participated in the survey.
• Note that the 18% is the data that comes from the survey.
EXAMPLE 2: Identify the population and sample.
• A survey of 2625 elementary school children found that 28% of the children could be classified as obese.
• Population: All elementary school children.
• Sample: The 2625 elementary school children surveyed.
Describing population and sample data
• Parameter: a numerical description of a population characteristic.
• This number must describe EVERYONE in a group
• Statistic: is a numerical description of sample characteristic.
• This number describes PART of a group.
EXAMPLE 3: Determine whether the numerical value is a parameter or a statistic.
• A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was \$ 125,000.
• The value \$125,000 is a statistic since this piece of data was taken from a subset of the alumni at a major university.
• The average salary of all assembly-line employees at a certain car manufacturer is \$ 33,000.
• The value \$33,000 is a parameter since this piece of data was taken from ALL assembly-line workers.
Branches of Statistics
• Descriptive statistics: the branch of statistics that involves the organization, summarization, and display of data.
• This happens when a piece of data is used to DESCRIBE a data set.
• Inferential statistics: the branch of statistics that involves using a sample to draw conclusions about a population.
• This happens when we make an INFERENCE about the piece of data.

EXAMPLE 4: Decide which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics?

• The chances of winning the California Lottery are one chance in twenty-two million.
• Descriptive: The chances of winning are 1 in 22 million.
• Inferential: Probably not the best game to win .
Types of Data
• Qualitative data: consist of attributes, labels, or non-numerical entries.
• Ex: Good, Bad, Strongly Agree. Anything that describes the quality of something.
• Quantitative data: consists of numerical measurements or counts.
• If a number is used as a label (zip code, SSN,…) this would be qualitative instead.
• The numbers on the shirts of a soccer team
• Qualitative (the number describes the member on the team)
• The number of seats in a movie theater
• Quantitative
Levels of Measurement
• Nominal: Data here are qualitative only. Data at this level are categorized using names, labels, or qualities. No mathematical computations can be made at this level.
• Ordinal: Can be either qualitative or quantitative. Data at this level can be arranged in order, or ranked, but differences between data entries are not meaningful
Levels of Measurement
• Interval: Can be ordered, and meaningful difference between data entries can be calculated. A zero entry simply represents a position on a scale; the entry is not an inherent zero.
• Inherent zero is a zero that implies “none.”
• Ratio: Similar to interval with the added property that a zero entry is an inherent zero. A ratio of two data values can be formed so that one data value can be meaningfully expressed as a multiple of another.
• To determine if data is Interval or Ratio, ask yourself if “twice as much” has any meaning.
EXAMPLE 6: Identify the data set's level of measurement.
• Hair color of women on a high school tennis team
• Nominal
• The average daily temperatures (in degrees Fahrenheit) on five randomly selected days: 21, 32, 30, 28, 31
• Interval
• The amounts of fat (in grams) in 44 cookies
• Ratio
• The ratings of a movie ranging from "poor" to "good" to "excellent"
• Ordinal