HEADS UP ON ENTROPY Statistics Project By Charles Cox and Maxcy Dimmick.

Slides:

Advertisements

Similar presentations

Statistics Unit 6.

Advertisements

1 The Islamic University of Gaza Civil Engineering Department Statistics ECIV 2305 ‏ Chapter 6 – Descriptive Statistics.

Cumulative Frequency Diagrams & Box Plots. Cumulative Frequency Time t minutes 0≤t

1. Statistics 2. Frequency Table 3. Graphical Representations  Bar Chart, Pie Chart, and Histogram 4. Median and Quartiles 5. Box Plots 6. Interquartile.

Starter 1.Find the median of Find the median of Calculate the range of Calculate the mode.

Quartiles & Extremes (displayed in a Box-and-Whisker Plot) Lower Extreme Lower Quartile Median Upper Quartile Upper Extreme Back.

Cumulative Frequency, Box Plots, Percentiles and quartiles.

Biostatistics Unit 3 - Graphs.

10. Presenting and analysing data * Averages for discrete data * Stem and leaf diagrams * Using appropriate averages * The quartiles * Measures of spread.

First Quantitative Variable: Ear Length  The unit of measurement for this variable is INCHES.  A few possible values for this first quantitative variable.

+ Review for Quarter 4 Test 2 LIII. Central Tendency LIV. Graphs.

Exploratory Data Analysis

1 Further Maths Chapter 2 Summarising Numerical Data.

Do Now Find the mean, median, mode, and range of each data set and then state which measure of central tendency best represents the data. 1)2, 3, 3, 3,

Bellwork 1. If a distribution is skewed to the right, which of the following is true? a) the mean must be less than the.

1 InterquartileRange Press Ctrl-A G Dear ©2010 – Not to be sold/Free to use Stage 4 Year 9.

Stem and Leaf Bingo. Pick 8 from the list

Cumulative frequency graphs

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Interpret stem-and-leaf plots, histograms, and box-and-whisker plots. Represent.

Represent sets of data using different visual displays.

Engineering Statistics KANCHALA SUDTACHAT. Statistics  Deals with  Collection  Presentation  Analysis and use of data to make decision  Solve problems.

Making sense of data We got to deal with some Math here folks.

Types of Graphs.

+ Review for Quarter 4 Test 2 LIII. Central Tendency LIV. Graphs.

The field of statistics deals with the collection,

Math 310 Section 8.1 & 8.2 Statistics. Centers and Spread A goal in statistics is to determine how data is centered and spread. There are many different.

Vocabulary to know: *statistics *data *outlier *mean *median *mode * range.

Cumulative frequency Cumulative frequency graph

Graphs Class A Class B. Pictograph Types of Graphs Line Graphs Plots Circle Graph Histogram Single Double Stem & Leaf Line Single Double Box - and - Whisker.

Box and Whisker Plots Example: Comparing two samples.

ALL ABOUT THAT DATA UNIT 6 DATA. LAST PAGE OF BOOK: MEAN MEDIAN MODE RANGE FOLDABLE Mean.

1. What is the first step in finding the median in a set of data? Write the numbers in order from least to greatest. 2.Find the mean using this data: 0,

Statistics Review  Mode: the number that occurs most frequently in the data set (could have more than 1)  Median : the value when the data set is listed.

Statistics and Probability - 1 What is the median of the data set? 2, 4, 2, 5, 6, 2, 5, 7, 8, 9, 11, 4, 6 a.2 b.5.5 c.5 d.6.

Figure 2-7 (p. 47) A bar graph showing the distribution of personality types in a sample of college students. Because personality type is a discrete variable.

Please copy your homework into your assignment book

Box-and-Whisker Plots

Line Plots & Box-and-Whiskers Plots

Chapter 6 – Descriptive Statistics

Cumulative Frequency Diagrams

Support for English, maths and ESOL Module 7: Developing the personal maths skills of teachers and assessors Master class 4: Handling data.

A statistical investigation

7. Displaying and interpreting single data sets

Measures of Central Tendency And Graphs

Name:_______________________ P - ___________ P - ___________

A technique for ordering numerical data

Box and Whisker Plots 50% Step 1 – Order the series.

Box-and-Whisker Plots

Range between the quartiles. Q3 – Q1

Section Ii: statistics

Box-And-Whisker Plots

Bellwork: Monday.

Warm Up # 3: Answer each question to the best of your knowledge.

Box-and-Whisker Plots

Box and Whisker Plots A.K.A Box Plots.

Please copy your homework into your assignment book

(-4)*(-7)= Agenda Bell Ringer Bell Ringer

Please copy your homework into your assignment book

Box-And-Whisker Plots

Box-And-Whisker Plots

Constructing a cumulative frequency table

Ticket in the Door GA Milestone Practice Test

Ticket in the Door GA Milestone Practice Test

Box-and-Whisker Plots

Displaying data in Stem-and-Leaf Plots and Histograms

Find the Mean of the following numbers.

Review of 6th grade material to help with new Statistics unit

Trials & laws & Large Numbers (Large Number Theory)

Presentation transcript:

HEADS UP ON ENTROPY Statistics Project By Charles Cox and Maxcy Dimmick

QUESTION What degree of entropy is introduced to the set of 50 pennies with one toss?

Rationale This simulation is an attempt to observe the Second Law of Thermodynamics, which states, “Nature favors entropy over disorder.” For the purpose of this experiment, we are defining entropy as a measure of disorder. We are modeling entropy with randomness.

Materials 50 pennies a tray or dish Paper Pencil graph paper.

Simulation Procedure 1) Turn all 50 pennies “heads up” in the tray. 2) Make one toss of the tray and allow pennies to fall on the tabletop or on the floor. 3) Record the number of pennies that landed “heads up.” 4) Repeat steps 1-3 for a total of 20 trials.

Entropy Scale The following scale is used to assess the degree of randomness or entropy in the set of fifty coins: heads: high degree of entropy or heads: moderate degree of entropy 0-10 or heads: low degree of entropy

Raw Data from Simulation Raw Data

Statistics from Simulation Mean: Median: 24 Mode: 24 Lower Extreme: 9 Upper Extreme: 41 Range: 32 Lower Quartile: 22 Upper Quartile: 31.5 Interquartile Range: 9.5 Number of Trials: 20

Stem and Leaf Number of Heads Generated by One Toss = 18 Heads

Box Plot

Frequency Table Number of Heads Generated by One Toss NumberFrequency

Histogram

Conclusion The results of this experiment suggest that a high degree of entropy is introduced to the set of coins by one toss. This conclusion is supported by several statistical elements. Both the median (24) and the mean (26.5) fall near the optimum number of heads for true randomness, which is 25. Also, a histogram of the data grouped by tens (roughly corresponding to the scale groupings) shows more trials falling in the “high degree of entropy” range than in all of the other categories combined.