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Words 957

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Words 957

Pages 4

Summarising data

Sample mean: x= Sample variance: s2 x 1 = n−1 n This has mean nθ and variance nθ(1 − θ). The Poisson distribution: p(x) = λx exp(−λ) for x = 0, 1, 2, . . . . x!

1 n

n

This has mean λ and variance λ. xi .

i=1

Continuous distributions n Distribution function: x2 i − nx

2

i=1

1 (xi − x) = n−1

2

. F (y) = P (X ≤ y) =

y

i=1

f (x) dx.

−∞

Sample covariance: g= 1 n−1 n Density function: 1 n−1 n (xi −x)(yi −y) = i=1 xi yi − nx y i=1 .

f (x) = Evaluating probabilities:

d F (x). dx

Sample correlation: r= g . sx sy

b

P (a < X ≤ b) = a f (x) dx = F (b) − F (a).

Probability

Addition law: P (A ∪ B) = P (A) + P (B) − P (A ∩ B). Multiplication law: P (A ∩ B) = P (A)P (B|A) = P (B)P (A|B). Partition law: For a partition B1 , B2 , . . . , Bk k k

Expected value:

∞

E(X) = µ =

−∞

xf (x) dx.

Variance:

∞ ∞

Var(X) =

−∞

(x − µ)2 f (x) dx =

−∞

x2 f (x) dx − µ2 .

Hazard function: h(t) = P (A|Bi )P (Bi ). i=1 f (t) . 1 − F (t)

P (A) = i=1 P (A ∩ Bi ) =

Normal density with mean µ and variance σ 2 : 1 f (x) = √ exp 2πσ 2 . Weibull density: f (t) = λκtκ−1 exp(−λtκ ) for t ≥ 0. Exponential density: − 1 2 x−µ σ

2

Bayes’ formula: P (A|Bi )P (Bi ) P (Bi |A) = = P (A) P (A|Bi )P (Bi ) k i=1

for x ∈ [−∞, ∞].

P (A|Bi )P (Bi )

Discrete distributions

Mean value: E(X) = µ = xi ∈S

f (t) = λ exp(−λt) for t ≥ 0. xi p(xi ). This has mean λ−1 and variance λ−2 .

Variance: Var(X) = xi ∈S

Test for population mean

(xi − µ)2 p(xi ) = xi ∈S

x2 p(xi ) − µ2 . i Data: Single sample of measurements x1 , . . . , xn . Hypothesis: H : µ = µ0 . Method: √ • Calculate x, s2 , and t = |x − µ0 | n/s. • Obtain critical value from t-tables, df = n − 1.

The binomial distribution: p(x) = n x θ (1 − θ)n−x for x = 0, 1, . . . , n. x…...

... B) [pic]= 0.7 C) [pic]= 0.6 D) [pic]= 0.5 ANSWER: D 14. Given a set of 25 observations, for what values of the correlation coefficient would we be able to say that there is evidence that a relationship exists between the two variables? A) [pic][pic] 0.40 B) [pic][pic] 0.35 C) [pic][pic] 0.30 D) [pic][pic] 0.25 ANSWER: A 15. If you are interested in comparing variation in sales for small and large stores selling similar goods, which of the following is the most appropriate measure of dispersion? A) The range B) The interquartile range C) The standard deviation D) The coefficient of variation ANSWER: D 16. Which of the following descriptive statistics is least affected by outliers? A) Mean B) Median C) Range D) Standard deviation ANSWER: B 17. Suppose you are told that the mean sample of numbers is below the median. This information suggests which of the following? A) The distribution is symmetric. B) The distribution is skewed to the right or positively skewed. C) The distribution is skewed to the left or negatively skewed. D) There is insufficient information to determine the shape of the distribution. ANSWER: C 18. Suppose you are told that sales this year are 30% higher than they were six years ago. What has been the average annual increase in sales over the past six years? A) 5.0% B) 4.5% C)......

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...TERM END EXAMINATIONS,MARCH-2013 BACHELOR OF COMMERCE, YEAR – III ELEMENTARY STASTISTICS Time: 3 hours M.Marks:60 SECTION A Note: - Attempt any 4 questions. All questions carry equal marks. (4 X 5) The answer should be limited upto 200 words. 1) What is statistics? Explain the nature and limitations of statistics? 2) What is frequency distribution? What are the different types of frequency distribution? 3) What is frequency curve? Explain cumulative frequency curve with example? 4) Suppose mean of a series of 5 item is30.four values are respectively, 10, 15, 30 and 35.estimate the missing 5th value of the series. ANSWER : Mean = (10+15+30+35+x)/5=30 Therefore, x=(30*50)-( 10+15+30+35) i.e x = 150-90, hence x=60 5) Calculate median of the following distribution of data. Class interval | 0-5 | 5-10 | 10-20 | 20-30 | 30-50 | 50-70 | 70-100 | frequency | 12 | 15 | 25 | 40 | 42 | 14 | 8 | n= 12+15+25+40+42+14+8=156 Hence median is at the average of n/2 & (n/2 +1) positon i.e 78th & 79th position Class interval | 0-5 | 5-10 | 10-20 | 20-30 | 30-50 | 50-70 | 70-100 | frequency | 12 | 15 | 25 | 40 | 42 | 14 | 8 | Position 12 27 52 92 134 148 156 6) Calculate the coefficient of correlation...

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...reliable statistics vary because there is no definitive count of the number of school-age children. About 60% of children who finish primary schools are boys, as the majority of girls rarely attend school for more than a few years. Children are often forced to work rather than attend school, particularly during planting or harvest periods. Since independence many steps have been taken and different commissions and committees have given suggestions to achieve universalization of Primary Education. But it is still far from the hope and the national target. Traditionally, parents have been reluctant to send their children to school. In the 1960s, the government sent the army to rural villages to compel school attendance and villagers hid their children, fearful of what would happen to them. More recently parents have failed to register their children's births to avoid later school enrollment. Head teachers, who are responsible for recruitment in rural areas, can be reluctant to travel outside their own villages to persuade parents to allow their children to attend school. In addition, nomadic children in the north of the country often do not have access to schools. STRUCTURE OF PRIMARY EDUCATION The structure of Niger primary education system starts with nursery from the age of five (5) to six (6). 6 years of elementary education is structured as follows: AGE | LEVEL | 7 years | Initiation level | 8 years | Preliminary/ preparatory level | 9 years | Elementary......

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...Unit 1 - Fundamentals of Statistics ReneeCarina Benavente American InterContinental University BUSN311-12005B-11 Abstract In many organizations surveys are done to determine the job satisfaction of their employees. Job satisfaction is important for theses organizations large or small because it makes the aspects of the job easy for employees. Analyzing the data within these surveys is to find the overall job satisfaction using qualitative and quantitative variables. Introduction A word wide study of job satisfaction has been assembled by a large organization called American Intellectual Union (AIU). I have been chosen to be a part of this massive global undertaking. I will be analyzing the data from this study and results survey using AIU’s data set. Chosen Variables In examining the data set and results of AIU’s employees I chose to analyze the positions of the employees as my qualitative variables and the intrinsic job satisfaction as my quantitative variables. I chose to analyze these two specific variables because as an hourly or salary paid employee their internal job satisfaction is very important to know. It is best to understand the job satisfaction of employee position within the organization to better the work environment. Qualitative and Quantitative Variables Using qualitative and quantitative variables you have to know and understand the difference between the two variable or the results would not add up. Quantitative data is data......

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...TERM END EXAMINATIONS,MARCH-2013 BACHELOR OF COMMERCE, YEAR – III ELEMENTARY STASTISTICS Time: 3 hours M.Marks:60 SECTION A Note: - Attempt any 4 questions. All questions carry equal marks. (4 X 5) The answer should be limited upto 200 words. 1) What is statistics? Explain the nature and limitations of statistics? 2) What is frequency distribution? What are the different types of frequency distribution? 3) What is frequency curve? Explain cumulative frequency curve with example? 4) Suppose mean of a series of 5 item is30.four values are respectively, 10, 15, 30 and 35.estimate the missing 5th value of the series. 5) Calculate median of the following distribution of data. Class interval | 0-5 | 5-10 | 10-20 | 20-30 | 30-50 | 50-70 | 70-100 | frequency | 12 | 15 | 25 | 40 | 42 | 14 | 8 | 6) Calculate the coefficient of correlation between the age of husbands and wives: Age of husband (yrs) | 21 | 22 | 28 | 32 | 35 | 36 | Age of wives (yrs) | 18 | 20 | 25 | 30 | 31 | 32 | SECTION B Note: -All questions are compulsory. Each Question carries equal mark. (40 X 1) 1) If a statistical series is divided into four equal parts, the end value of each part is called a ……… a. Quartile b. Deciles c. Percentiles d. Range 2)......

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...Average and mean are used interchangeably to label the result of the sum of all measurements divided by the number of measurements. In mathematical notation the formula for calculating the sample mean is given below. x=x1+x2+…+xnn=i=1nxin If the value given represents the mean of all values in a population it is denoted μ. When the data are from a sample, the calculated value, in this case the mean, is referred to as a statistic. When the data represent the entire population, the value is referred to as a parameter. The primary goal of this course is to learn techniques for which we will use sample statistics to estimate or make inference about parameters. Example 1: Compute the mean of the list of numbers: 1, 5, 7, 10, 12 Answer: x=1+5+7+10+125=355=7 Example 2: In the Spring 2012 Elementary Statistics, 161 students submitted a valid numeric value, denoted xi , for the number of texts in the month prior to the date this data was collected and i=1161xi=251,832. The average number of texts in the month prior for the Spring 2012 Elementary Statistics class at ACPHS was _____________________________ Example 3: The MHEALTH.xlsx contains data for 40 male patients. Denote the variable for BMI (body mass index) as xi . Suppose i=140xi=1,039.9. The mean BMI in the male patients in this data set is _____________________. Example 4: A meta-analysis study is underway to assess the number of cigarettes smoked on a typical day for college freshman who smoke. If one...

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... MA3110 Statistics Dr. P. A. Williams What is my meaning of Statistics? My meaning or definition of statistics is that of its base word itself. Stat. Along with other elements that would make it a definition or an opinion of sort, but I’m sure that I won’t be far from what others may say it means or what they think it means. Stat is defined as with no delay; at once. When most of us think about statistics, we think of comparisons, of two or more entities but ones balance might be more or less as well as winning and losing. There is still that scale that separates the two where one is ahead of the other. The people analyzing and drawing conclusions are getting this information have to get it out to those that follow up on whatever the subject may be fast because people want to know. It’s said that Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on data according to (Pearson’s Elementary Statistics Using Microsoft Excel by, Mario F. Triola). This is the same as I said without including all of the other tools needed, or used in Statistics. Television shows are another example being on statistic radar so to speak. You have so many television shows that are out right now, but how do we know......

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...This paper will explain what statistics are. Statistics are used in so many ways, including business. This paper will thoroughly defining statistics, the types and levels of statistics, the role of statistics in a business and examples of how statistics may be used. The most common definition for statistics would be the collection of numerical data. Examples of numerical data could be the percentage of how many African-Americans passed, dropped out or failed out of high school in Vallejo, CA in 2013. Another would be how many slam dunks did LeBron James have last year or asking how many assist did LeBron James average last season; would give you numerical data. In this coarse, statistics is described as the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions. Statistics are usually divided into two catagories, descriptive and inferential statistics. Discriptive statistics are the methods of organizing, summarizing and presenting data in an informative way. Inferential statistics (also known as statistical inference) are the methods used to estimate a property of a population on the basis of a sample. There are two variables/attributes involved in statistics, qualitative and quantitative. Qualitative variables are when the characteristics being studied are categorical or nonnumeric. Quantitative variables are when a variable is studied and the study describes how much or how many. There are four......

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...13 April 2014 Elementary Education: To Give Homework or To Not Give Homework Mankind is constantly observing and learning. The brain is constantly retaining information whether related to academics or simply everyday life. The subject matter of what one learns and the methods of how one learns is vital. Teachers play a crucial part in one’s life. They determine and guide much of their students’ future. Every little detail of teaching impacts the students. How teachers incorporate and reinforce learning outside of the classroom is extremely influential as well. The debate regarding assigning homework is thoroughly discussed and argued among educators across America. Elementary education is an intriguing occupation that debates the topic of assigning homework, which I believe should be assigned depending on the student’s age. Elementary education is an intriguing and rewarding occupation. The Bible regards teaching as a very highly respected and crucial role that honors God’s values of love, compassion, and truth. Teachers have an opportunity to directly influence and impact children in a positive manner. Many students remember their teachers throughout their elementary years. Those years, during one’s childhood, are formative as beliefs and ideas taught at a young age often carry into the future. Also, elementary education is a beneficial way to give back to the world by increasing knowledge and advocating learning. Teachers often experience a renewed spirit after......

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...IN STATISTICS REGRESSION ANALYISIS Seventh Edition William Mendenhall University of Florida Terry Sincich University of South Florida Prentice Hall Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Toronto Madrid Delhi Milan Mexico Munich City Sao Paris Paulo Montreal Sydney Hong Kong Seoul Singapore Taipei Tokyo Editor in Chief: Deirdre Lynch Acquisitions Editor: Marianne Stepanian Associate Content Editor: Dana Jones Bettez Senior Managing Editor: Karen Wernholm Associate Managing Editor: Tamela Ambush Senior Production Project Manager: Peggy McMahon Senior Design Supervisor: Andrea Nix Cover Design: Christina Gleason Interior Design: Tamara Newnam Marketing Manager: Alex Gay Marketing Assistant: Kathleen DeChavez Associate Media Producer: Jean Choe Senior Author Support/Technology Specialist: Joe Vetere Manufacturing Manager: Evelyn Beaton Senior Manufacturing Buyer: Carol Melville Production Coordination, Technical Illustrations, and Composition: Laserwords Maine Cover Photo Credit: Abstract green ﬂow, ©Oriontrail/Shutterstock Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps. Library of Congress Cataloging-in-Publication Data Mendenhall, William. A second course in statistics :......

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...Sidney Smith 01/24/2015 CH 2 HW Statistics 2-1 1. Five reasons for organizing data into a frequency distribution: a. To organize the data in a meaningful, intelligible way. b. To enable the reader to determine the nature or shape of the distribution. c. To facilitate computational procedures for measures of average and spread. d. To enable the researcher to draw charts and graphs for the presentation of data. e. To enable the reader to make comparisons among different sets. 2. Categorical Frequency Distributions is used for data that can be placed in specific categories. Grouped Frequency Distributions is used when the range of the data is large and the data must be grouped in to classes that are more than one unit in width. Ungrouped Frequency Distribution is used when the range of data has been organized into a frequency distribution and analyzed by looking for peaks and extreme values. (Cumulative Frequency Distribution is a distribution that shows the number of data values less than or equal to a specific value (usually an upper boundary).) 3. A frequency distribution should have five to twenty classes. Class width should be an odd number so that the midpoints of the classes are in the same place values as the data. 4. An Open Ended Frequency Distribution has either a first class with no lower limit or a last class with no upper limit. They are necessary to accommodate all the data. Class Boundaries Midpoint Width 5. 42.5-47.5 45 5 6. 124.5-131.5 128 7 7. 8.235-11.365 9.8...

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...Basics of Statistics Jarkko Isotalo 30 20 10 Std. Dev = 486.32 Mean = 3553.8 N = 120.00 0 2400.0 2800.0 2600.0 3200.0 3000.0 3600.0 3400.0 4000.0 3800.0 4400.0 4200.0 4800.0 4600.0 5000.0 Birthweights of children during years 1965-69 Time to Accelerate from 0 to 60 mph (sec) 30 20 10 0 0 Horsepower 100 200 300 1 Preface These lecture notes have been used at Basics of Statistics course held in University of Tampere, Finland. These notes are heavily based on the following books. Agresti, A. & Finlay, B., Statistical Methods for the Social Sciences, 3th Edition. Prentice Hall, 1997. Anderson, T. W. & Sclove, S. L., Introductory Statistical Analysis. Houghton Miﬄin Company, 1974. Clarke, G.M. & Cooke, D., A Basic course in Statistics. Arnold, 1998. Electronic Statistics Textbook, http://www.statsoftinc.com/textbook/stathome.html. Freund, J.E.,Modern elementary statistics. Prentice-Hall, 2001. Johnson, R.A. & Bhattacharyya, G.K., Statistics: Principles and Methods, 2nd Edition. Wiley, 1992. Leppälä, R., Ohjeita tilastollisen tutkimuksen toteuttamiseksi SPSS for Windows -ohjelmiston avulla, Tampereen yliopisto, Matematiikan, tilastotieteen ja ﬁlosoﬁan laitos, B53, 2000. Moore, D., The Basic Practice of Statistics. Freeman, 1997. Moore, D. & McCabe G., Introduction to the Practice of Statistics, 3th Edition. Freeman, 1998. Newbold, P., Statistics for Business and......

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...linear correlation between the two given variables. Solve the following problems: Listed below are baseball team statistics, consisting of the proportions of wins and the result of this difference: Difference (number of runs scored) - (number of runs allowed). The statistics are from a recent year, and the teams are NY—Yankees, Toronto, Boston, Cleveland, Texas, Houston, San Francisco, and Kansas City. Difference 163 55 –5 88 51 16 –214 Wins 0.599 0.537 0.531 0.481 0.494 0.506 0.383 o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics. Use α = 0.05. o Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins and the above difference? A classic application of correlation involves the association between temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 minute and the corresponding temperatures in °F: Chirps in 1 Min 882 1188 1104 864 1200 1032 960 900 Temperature(°F) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6 o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics. Use α = 0.05. o Is there a linear correlation between the number of chirps in 1 minute and the temperature?......

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...Introductory STATISTICS 9TH EDITION This page intentionally left blank Introductory STATISTICS 9TH EDITION Neil A. Weiss, Ph.D. School of Mathematical and Statistical Sciences Arizona State University Biographies by Carol A. Weiss Addison-Wesley Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo On the cover: Hummingbirds are known for their speed, agility, and beauty. They range in size from the smallest birds on earth to several quite large species—in length from 2 to 8.5 inches and in weight from 0.06 to 0.7 ounce. Hummingbirds ﬂap their wings from 12 to 90 times per second (depending on the species) and are the only birds able to ﬂy backwards. Normal ﬂight speed for hummingbirds is 25 to 30 mph, but they can dive at speeds of around 60 mph. Cover photograph: Hummingbird, Editor in Chief: Deirdre Lynch Acquisitions Editor: Marianne Stepanian Senior Content Editor: Joanne Dill Associate Content Editors: Leah Goldberg, Dana Jones Bettez Senior Managing Editor: Karen Wernholm Associate Managing Editor: Tamela Ambush Senior Production Project Manager: Sheila Spinney Senior Designer: Barbara T. Atkinson Digital Assets Manager: Marianne Groth Senior Media Producer: Christine Stavrou Software Development: Edward Chappell, Marty Wright C iDesign/Shutterstock Marketing Manager: Alex Gay Marketing......

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...Testing in elementary school is unfortunate. Students should not be required to start testing in kindergarten because kids are not allowed to learn social skills and enjoy school. This is a time where students should be allowed to have free play. Free play is a valuable time to allow kids to time to develop their social skills. Parents and teachers should form a rally to bring back free play. Standardized test is a high stake testing that is causing havoc in the education industry. How and why do they think it is appropriate to start testing so early in the education? Is there any valuable to common core test? When will the school district provide adequate infrastructures in the schools to support the computerized testing? There are tons of unanswered questions…. We need support in the school systems immediately. Why have they turned things into political debates regarding children educations? Testing is overrated and does not prove what a child is capable of doing. When are states going to hold parents accountable for not teaching basic skills at home? Why are schools not allowed to require kids to stay home until a parent conference when they are causing physical harm to educators and causing disruptions in the class? This is frustrating and overwhelming to teachers and students. It is hindering the learning environment. Parents should be held liable for not teaching kids at home and being supportive to the education environment. I hope all educators will take a stand in......

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