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.

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

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

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