+ Chapter 1

+ Chapter 1 Section 1: Overview of Statistics

+ Ch 1: Introduction to Statistics What is Statistics? What words come to mind when you hear the word statistics? Where have you seen statistics?

+ Statistics: The science of collecting, organizing, analyzing, and interpreting data in order to make decisions. Words that might come to mind: data, percents, means, averages, surveys, polls, graphs, and charts. Places you might have seen them: advertisements, sports, articles, newspapers, and research journals.

+ Branches of Statistics Descriptive Statistics: the branch of statistics that involves organizing, summarizing, and displaying data. Keyword: DESCRIBE

+ Examples of Descriptive Statistics Looking at the percent of each color M&M. Collecting data on how many pets are in households in your neighborhood.

+ Inferential Statistics The branch of statistics that involves using a sample to draw conclusions or generalizations about a population.

+ Examples of Inferential Statistics Taking a sample of M&Ms then making an inference that there’s a higher percent of blue M&Ms. Doing a study to see if there is a connection between eating breakfast and doing well in school.

+ Data Consist of information coming from observations, counts, measurements, or responses. The singular for data is datum.

+ Examples of Data Observing students’ hair color. Measuring students’ height. Surveying students on their favorite TV show.

+ Population The collection of ALL outcomes, responses, measurements, or counts of interest. Ex: All seniors at SHS.

+ Sample A subset of a population Ex: Students in this class would be a sample of all senior in SHS.

+ Parameter A numerical description of a population characteristic. Ex: Weight of all seniors at SHS.

+ Statistics A numerical description of a sample characteristic. Ex: Weight of students in this class would be a statistic if the population was all seniors at SHS.

+ Chapter 1 Section 2: Types of Data

+ Data Lists America League Baseball Teams: Boston Red Sox, Chicago White Sox, Cleveland Indians, Detroit Tigers Report Card Grades: A+, A, A-, B+, B, B- Average Temperature in Shrewsbury in each month: 31, 34, 43, 54, 66, 74, 79, 78, 69, 59, 47, 36 Prices of Concert Tickets: $50, $40, $25, $75, $69, $48, $99

+ Look at Each Data List Is there a meaningful order you can put the data in? Is it meaningful to subtract one data value from another? If the list contains numerical data, what does zero mean? If the list contains numerical data, can a ratio of two values be formed?

+ Nominal Level of Measurement: Data at this level are categorized using names, labels, or qualities. So it’s qualitative only. No mathematical computations can be made. Ex: Eye color, Team’s names, Hair color.

+ Ordinal Level of Measurement: Data that represents categories that have an associated order (often ranking.) Standard mathematical operations are not defined for ordinal data. Examples: Giving a rating to your service at a fast food restaurant as very good, good, fair, bad, or very bad. Number of stars a movie gets.

+ Interval Level of Measurement: If the data can be ordered and the arithmetic difference is meaningful. At the interval level, a zero entry simply represents a position on a scale. The entry is not a meaningful zero. Ex: Water temperature, years on a timeline

+ Ratio Level of Measurement: Similar to interval data, except that it has a meaningful zero point and the ratio of two data points is meaningful. One data value can be expressed as a multiple of another. If one person weighed 100 lbs and another person weighs 200 lbs the 200 lb person weighs twice as much, a 1:2 ratio. Ex: Students’ height or weight.

+ Categorical (Qualitative Data) Consist of attributes or labels. Ex: Eye color, baseball teams

+ Could categorical data consist of numbers?

+ YES! Phone numbers Jersey numbers Social security numbers The above examples are all numbers that are labels.

+ Quantitative Data Consist of numerical measurements or counts. Ex: Heights of Students, Weights of Chairs, Time waiting at red lights

+ Discrete Data: Data in which the observations are restricted to a set of values that possess gaps. Ex: Data values that are prices: $2.34, $2.48, $2.99, $3.56, and $3.26. Data values that are whole numbers, number of pets: 1, 3, 2, 1, 0, 1, 2, 1, 1, 2, 2

+ Continuous Data: Data that can take on any value within some interval. Ex: The data values of the length of a sofa. Any value between 0-15 feet. Weight of a dog pounds.

+ Chapter 1 Section 3: Experimental Design

+ Guidelines of a Statistical Study Identify the variable(s) of interest and the population of the study. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population. Collect the data. Describe the data using descriptive statistic techniques. Interpret the data and make decisions about the population using inferential statistics. Identify possible errors.

+ Data Collection The average number of pets students in this class own. The average amount a freshman in college in the US spends on tuition. The average speed vehicles travel in the morning coming to school. The number of times you will get heads when you flip a coin 1000 times. The time it would take for a forest fire to spread through a community.

+ For each situation think about how you would collect the data.

+ Taking a Census A census is a count or measure of an entire population. Taking a census provides complete information, but is often costly and difficult to perform.

+ Use Sampling A sampling is a count or measure of part of a population. The statistics calculated from a sample are used to predict various population parameters. Using sampling is often more practical than a census.

+ Use a Simulation A simulation is the use of a mathematical or physical model to reproduce the conditions of a situation or process. Computers usually collect the data. The simulation allows you to study situations that are impractical or dangerous in real life.

+ Perform an Experiment In an experiment, a treatment is applied to part of a population and responses are observed. The experimental group is the group that receives the treatment. The control group is the group that doesn’t receive the treatment or they might get a placebo, a fake treatment. Both groups are observed and the results are compared.

+ Types of Samples

+ Simple Random Sample A sample in which every possible sample of the same size has an equal chance of being selected. One way to do this is to assign numbers to each member of the population and then let a computer create a random number table.

+ Stratified Sample Used when you want to have members from each segment of a population. The population is divided into two or more subsets, strata. A sample is then randomly selected from each of the strata, guaranteeing each subset is represented in the sample.

+ Cluster Sample Used when the population falls into naturally occurring subgroups, each having similar characteristics. The cluster sample is created by dividing the population into groups, clusters, then selecting one or more of the clusters. It is important that all of the clusters have the same characteristics.

+ Systematic Sample A sample in which each member of the population is assigned a number. The population is then ordered in some way and then the sample members are selected at regular intervals from a starting number.

+ Convenience Sample Consists only of available people. This type of sampling is not recommended because it often leads to biased studies.