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STA 2023

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

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  1. STA 2023 Chapter 1 Notes

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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 .

  9. 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.

  10. EXAMPLE 5: Determine whether the data are qualitative or quantitative. • 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

  11. 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

  12. 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.

  13. 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

  14. Table Summary

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