Introduction to Statistics: Data, Sampling, and Descriptive Statistics, Schemes and Mind Maps of Linear Algebra

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Introduction to Statistics

An Overview of Statistics

Populations & Samples

Example : In a recent survey, 250 college students at Union College were asked if they smoked cigarettes regularly. 35 of the students said yes. Identify the population and the sample. Responses of all students at Union College (population) Responses of students in survey (sample)

Parameters & Statistics

A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic. Parameter (^) Population Statistic (^) Sample

Branches of Statistics

The study of statistics has two major branches: descriptive statistics and inferential statistics. Statistics Descriptive statistics Inferential statistics Involves the organization, summarization, and display of data. Involves using a sample to draw conclusions about a population.

Descriptive and Inferential Statistics

Example : In a recent study, volunteers who had less than 6 hours of sleep were four times more likely to answer incorrectly on a science test than were participants who had at least 8 hours of sleep. Decide which part is the descriptive statistic and what conclusion might be drawn using inferential statistics. The statement “four times more likely to answer incorrectly” is a descriptive statistic. An inference drawn from the sample is that all individuals sleeping less than 6 hours are more likely to answer science question incorrectly than individuals who sleep at least 8 hours.

Types of Data

Data sets can consist of two types of data: qualitative data and quantitative data. Data Qualitative Data Quantitative Data Consists of attributes, labels, or nonnumerical entries. Consists of numerical measurements or counts.

Qualitative and Quantitative Data

Example : The grade point averages of five students are listed in the table. Which data are qualitative data and which are quantitative data? Student GPA Sally 3. Bob 3. Cindy 2. Mark 2. Kathy 3. Qualitative data Quantitative data

Nominal Level of Measurement

Data at the nominal level of measurement are qualitative only. Levels of Measurement Nominal Calculated using names, labels, or qualities. No mathematical computations can be made at this level. Colors in the US flag Names of students in your class Textbooks you are using this semester

Ordinal Level of Measurement

Data at the ordinal level of measurement are qualitative or quantitative. Levels of Measurement Arranged in order, but differences between data entries are not meaningful. Class standings: freshman, sophomore, junior, senior Numbers on the back of each player’s shirt Ordinal Top 50 songs played on the radio

Ratio Level of Measurement

Data at the ratio level of measurement are similar to the interval level, but a zero entry is meaningful. Levels of Measurement A ratio of two data values can be formed so one data value can be expressed as a ratio. Ages Grade point averages Ratio Weights

Summary of Levels of Measurement

Nominal Yes No No No Ordinal Yes Yes No No Interval Yes Yes Yes No Ratio Yes Yes Yes Yes Determine if one data value is a multiple of another Subtract data values Arrange data in order Put data in categories Level of measurement

Designing a Statistical Study

GUIDELINES

1. Identify the variable(s) of interest (the focus) and the population of the study.
2. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population.
3. Collect the data.
4. Describe the data.
5. Interpret the data and make decisions about the population using inferential statistics.
6. Identify any possible errors.

Methods of Data Collection

In an observational study , a researcher observes and measures characteristics of interest of part of a population. In an experiment , a treatment is applied to part of a population, and responses are observed. A simulation is the use of a mathematical or physical model to reproduce the conditions of a situation or process. A survey is an investigation of one or more characteristics of a population. A census is a measurement of an entire population. A sampling is a measurement of part of a population.