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STA 2023 Chapter 1 Notes

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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.

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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.

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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.

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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.

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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.

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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.

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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 .

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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.

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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

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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

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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.

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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

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Table Summary Level of Measurement Put data in categories Arrange data in order Subtract data values Determine if one data is a multiple of another Nominal YesNo Ordinal Yes No Interval Yes No Ratio Yes

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