Introduction to Statistics

Objectives

• Define statistics and its key concepts.

• Distinguish between a population and a sample, and between a parameter and a statistic.

• Differentiate between descriptive and inferential statistics.

Definition of Statistics

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions.

Data

Data consists of information coming from observations, counts, measurements, or responses.

• Example:

  • 7 in 10 Americans believe the arts unify their communities.

  • 21% of 8–11 year-olds have a social media profile.

Data Sets

• Population: The collection of all outcomes, responses, measurements, or counts that are of interest.

• Sample: A subset, or part, of the population.

Example: Identifying Data Sets

In a survey, 834 employees in the U.S. were asked if they thought their jobs were highly stressful. Of the 834 respondents, 517 said yes.

• Population: All employees in the U.S.

• Sample: The 834 employees surveyed.

• Sample Data Set: 517 "yes" and 317 "no" responses.

Parameters and Statistics

Parameter

• A parameter is a numerical description of a population characteristic.

• Example: Average age of all people in the United States.

Statistic

• A statistic is a numerical description of a sample characteristic.

• Example: Average age of people from a sample of three states.

Example: Distinguishing Parameter and Statistic

• If a survey of 9400 individuals finds an average of 5.19 hours per day spent in leisure, this is a statistic (since it is based on a sample).

• If the average SAT math score for an entire freshman class is 514, this is a parameter (since it is based on the whole population).

• If 34% of stores in a sample were not storing fish at the proper temperature, this is a statistic.

Branches of Statistics

Descriptive Statistics

• Involves the organization, summarization, and display of data.

• Examples: Tables, charts, averages.

Inferential Statistics

• Involves using sample data to draw conclusions about a population.

Example: Descriptive and Inferential Statistics

• A study of 1502 U.S. adults found that 18% of adults from households earning less than $30,000 annually do not use the Internet.

• Population: All U.S. adults.

• Sample: 1502 adults surveyed.

• Descriptive: "18% of adults from households earning less than $30,000 do not use the Internet."

• Inferential: The Internet may be less accessible to lower-income households.

Chapter 1.2: Data Classification

Objectives

• Distinguish between qualitative and quantitative data.

• Classify data by the four levels of measurement: nominal, ordinal, interval, and ratio.

Types of Data

• Qualitative Data: Consists of attributes, labels, or nonnumerical entries.

  • Examples: Major, place of birth, eye color.

• Quantitative Data: Consists of numerical measurements or counts.

  • Examples: Age, weight, temperature.

Example: Classifying Data by Type

The following table shows sports-related head injuries treated in U.S. emergency rooms:

• Qualitative Data: Types of sports (nonnumerical entries).

• Quantitative Data: Number of head injuries (numerical entries).

Levels of Measurement

Nominal Level

• Qualitative data only.

• Data are categorized using names, labels, or qualities.

• No mathematical computations can be made.

Ordinal Level

• Qualitative or quantitative data.

• Data can be arranged in order, or ranked.

• Differences between data entries are not meaningful.

Interval Level

• Quantitative data.

• Data can be ordered.

• Differences between data entries are meaningful.

• Zero represents a position on a scale, not an inherent zero (zero does not mean "none").

Ratio Level

• Quantitative data.

• Similar to interval level, but zero entry is an inherent zero (implies "none").

• Ratios of data values can be formed.

• One data value can be expressed as a multiple of another.

Example: Classifying Data by Level

Example: Interval vs. Ratio Level

Summary Table: Four Levels of Measurement

Examples of Data Sets and Calculations

Key Formulas and Notation

• Population parameter: (mu) for mean, (sigma) for standard deviation.

• Sample statistic: (x-bar) for mean, for standard deviation.

Summary

• Statistics is the science of data collection, analysis, and interpretation.

• Populations and samples are fundamental concepts; parameters describe populations, statistics describe samples.

• Data can be qualitative or quantitative, and classified by four levels of measurement: nominal, ordinal, interval, and ratio.

• Descriptive statistics summarize data; inferential statistics draw conclusions about populations from samples.