Statistics+2

= = Statistics 2 Bryan (group leader), Calvin, Bionca and Matt.
 * Group 11** __**MARKED**__

Statistics is the mathematical science of collection, analysis, interpretation, explanation and presentation of data. Statistics also provides tools for forcasting a set of data.

Common ways of collecting statistics: Charts/Tables,Lines of best fit Graphs, Scatter plots,Extrapolation/Interpolation/Correlation **__Lines of Best Fit__** Line of Best Fit Rules 1. Count up the co-ordinates 2. Place your linear line with the **trend!!!** 3. Place the same number of points above the line, and the same number of points below the line. 4. Don't count the points on the line or the outliers. **__History of Statistics:__**
 * A line of best fit is a __**staight**__ line that is drawn on a scatter plot to show the basic trend of the data
 * On a scatter plot **DO NOT CONNECT** the dots to make the line of best fit! In a rare case, you may have to connect all of they points due to the pattern that the graph is going
 * The line of best that rises quickly from left to right is called a **positive correlation**.
 * The line of best that falls down quickly from left to the right is called a **negative correlation**
 * **Strong** positive and negative correlations have data points very close to the line of best fit..
 * **Weak** positive and negative correlations have data points that are not clustered near the line of best fit.
 * Data points that are not close to the line of best fit are called **outliers**.

= = **__Interpolation and Extrapolation__** **Interpolation** is a process of determining a value(s), from the line of best fit. Interpolation is used within the cluster of the data Extrapolation is used on a line of best bit that EXTENDS further than the given points.
 * Extrapolation** is a process of finding a value(s) from the line of best fit. Extrapolation is similar to interpolation, but they are not quite the same.
 * Special Note** __Interpolation__ is usually more accurate, because you are using the already given data to estimate. With extrapolation there is always the chance the data may change at any given time. [[file:interpolation and extra.ppt]]

**__Correlation__**
 * It indicates the strength and direction of a linear relationship between two or more unknown variables
 * How big the relationship is between the data
 * Shows what direction the line of best fit would travel (positive, negative, none, strong, weak)

**__Direction__** No Correlation: When a set of data is __not__ related in any way Positive Correlation: When the set of data shows relativity and the line of best fit points up and to the right Negative Correlation: When the set of data shows relativity but the line of best fit points down and to the right

High correlation(is better if you want to interpolate and extrapolate): The point of data fall near to the line of best fit. Low correlation: the points of data fall quite far from the line of best fit. No correlation: No line of best fit can be drawn.
 * __Strength__**

Extrapolate the //y// value when //x// = 2.3. (0.3 0.80), (0.7, 1.3), (1.2, 2.0), (1.8, 2.7) The line of best fit is //y// = 1.27778 //x// + 0.42222, and therefore the value at 2.3 is 3.3611.
 * __Example of Extrapolation__**

2007 TEAM STATS Chargers
for the above table, this is what a graph looks like before is made into a scatter plot Knill, G. (1999). //MathPower 9//. Dian Wyman Mr. T Pages Notes
 * Total First Down || 321 ||
 * First Downs (Rushing-Passing-By Penalty) || 137 - 169 - 15 ||
 * Third Down || 92-213 ||
 * Fourth Down || 6-011 ||
 * Total Offensive Yards || 5840 ||
 * Offense (Plays-Average Yards) || 1016 - 5.7 ||
 * Total Rushing Yards || 2582 ||
 * Rushing (Plays-Average Yards) || 521 - 5.0 ||
 * Total Passing Yards || 3258 ||
 * Passing (Comp-Att-Int-Avg) || 287 - 466 - 9 - 11.4 ||
 * Sacks Taken || 29 ||
 * Defensive Sacks || 61.0 ||
 * Touchdowns || 59 ||
 * __//Works sited //__**