Statistics and Organization of Data Statistics: The gathering, organizing, analyzing, and presentation of numerical information Variable: Any particular quantity that is subject to change, and is being controlled or measured in a study Raw Data: Unprocessed information collected by a study

Example: Recall the Monty Hall experiment:

Variables: The process itself: Either keep or change doors (controlled) The number of trials (controlled) The number of wins (measured) Raw Data: The table of results from each group Statistics: The estimated probability of winning Average number of wins per group etc.

Discrete Variable: A measurand that takes on only discrete values (usually Whole numbers). Example: The number of “yes” votes in a referendum Continuous Variable: A measurand that can take on a Real number value. Example: The height of any individual student in this class Two different types of variables:

Statistics also means the organization and presentation of data. A Frequency Diagram is a useful tool for presenting the number of occurrences of each value or range of values of the variable being measured. Example: Create a bar chart that presents the distribution of student birthdays, according to season

A Tally-table The descriptive labels “Spring”, “Summer”, etc identify this as categorical (rather than numerical) data

Example: Use Excel to simulate rolling a pair of dice 500 times, and compare the frequency of each roll value (from 2 to 12) 500 data points Here is a sample of the raw data. Does it tell much of a story?

A bar chart with numerical categories is called a Histogram The chart clearly shows that rolling 6, 7, or 8 is much more likely than 2 or 12

A Frequency Polygon is like a histogram, except a line chart is drawn instead of a bar chart

Eg: 9% of rolls gave a total roll value of 9 A Relative Frequency Histogram plots the percentage of occurrences of each value

A Cumulative Frequency Polygon shows the total percentage up to a certain value Eg: 83% of rolls total 9 or less

A Pie Chart is useful to illustrate a comparison of categories that make up portions of a “whole”

A pictograph uses a kind of icon to add visual impact

Sometimes, especially with continuous data, it is necessary to group data into “bins” in order to create a histogram. Example: Consider the table of students’ averages:

Where does data come from? Measurement Survey OMG! The Internet!

Data from the Internet should be scrutinized for its veracity. Can the data be trusted? How reliable is the source? Government websites are usually reliable: Look for domain names:.gc.ca.gov Example: Analyze daily maximum temperature data from last month from

Another great website for data: