...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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...Statistics formula sheet 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...
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...CHAPTER 3 Describing Data: Numerical Multiple-Choice Questions 1. A scatter plot can illustrate all of the following except: A) The median of each of the variables. B) The range of each of the variables. C) An indication of outliers. D) Patterns of values. ANSWER: A 2. For the following scatter plot, what would be your best estimate of the correlation coefficient? A) -0.8 B) -1.0 C) -0.3 D) 0.0 ANSWER: A 3. For the following scatter plot, what would be your best estimate of the correlation coefficient? A) 1.0 B) 0.8 C) 0.3 D) 0.0 ANSWER: B 4. Calculate the correlation for the following (X, Y) data: (53, 37), (34, 26), (10, 29), (63, 55), (28, 36), (58, 48), (28, 41), (50, 42), (39, 21), and (35, 46). A) 0.710 B) 100.6 C) 0.670 D) 0.590 ANSWER: D 5. Suppose that we are interested in exploring the determinants of successful high schools. One possible measure of success might be the percentage of students who go on to college. The teachers’ union argues that there should be a relationship between the average teachers’ salary and high school success. The following equation of the regression line is obtained: “% of students going on to college = 13 + 0.001Average Teachers’ Salary” Which of the following statements is true? A) Increase % of students going on to college by 0.001 percent, we would expect average teacher’s...
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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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...classes visit www.snaptutorial.com Resources: University Library and the Internet Select a research issue, problem, or opportunity facing a Learning Team member’s organization to examine using hypothesis testing and a regression analysis on the collected data. Write a 1,050- to 1,750-word paper describing a new hypothesis test using a different statistic (e.g., large sample size, small sample size, means and/or proportions, one- and two-tailed tests) to perform on that data. Formulate a new hypothesis statement and perform the five-step hypothesis test on the data. Describe the results of the tests. Interpret the results of the regression analysis, state the limitations of the analysis, and describe the significance of the results to the organization. Be sure to attach the results of the regression analysis created in Microsoft® Excel to your paper. Present the results to the class in a 10-minute PowerPoint® presentation ----------------------------------------------- MTH 233 Week 2 Individual Assignment Individual Assignment 1 For more classes visit www.snaptutorial.com Resources: Ch.1 & 2 of Elementary...
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...Unit 1 - Fundamentals of Statistics Kathtrina Brazell American InterContinental University October 12, 2014 Abstract The purpose of this essay is to examine two of the nine sections of data and include all data points listed in the column for the variable. All of these items will be used to combine into one comprehensive report. Introduction In this assignment I will one section of qualitative data (choose either Gender or Position) one section of quantitative data (choose either Intrinsic or Extrinsic) and provide data. In each section the data will be indentified and the reason for the selection will be stated. Charts and graphs will be provided. An explanation of the importance of charts and graphs will be stated. Chosen Variables The variables that I chose to analyze are gender for my qualitative variable and Intrinsic for my quantitative variable. Difference in variable types “Qualitative data are no numerical measurements of characteristics, such as hair color or the charge of electron. Quantitative data are numerical measurements like weight, height, and age. The two data types need to be handled differently because qualitative characteristics don't have clear mathematical relationships to one another.” (Elementary Statistics) Descriptive statistics: Qualitative variable |Position |Tenure |Job Satisfaction |Intrinsic | |1 |3 |4.9 |6.4 | |1 ...
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...Unit 1 - Fundamentals of Statistics Patricia Schneider American InterContinental University Abstract This paper is about the difference between qualitative data and quantitative data. If also will show how a qualitative data chart looks like and how the information is retrieved, it shows what type of information is put in a quantitative chart and how it is also retrieved. What standard deviation and variance is? Why charts and graphs are important tool for communicating facts and figures? Introduction The data that I chose for the qualitative data was the gender, and the quantitative data that I chose was the intrinsic. In this essay you will learn what the differences between qualitative data and quantitative data is? Why graphs and charts are so important in businesses and why they are used in communicating the facts? Chosen Variables The data that I have chosen is the gender and the intrinsic. The gender is qualitative data and the intrinsic is the quantitative data. Difference in variable types The difference between qualitative and quantitative variables is the qualitative has no value or is just a label where the quantitative has a value. The qualitative is a label there is no value of information to be measured. Qualitative is a non numerical measurement on a set of people or objects (Segal, 2011). Quantitative is numerical measurement for a set of people or objects (Segal, 2011). Descriptive statistics: Qualitative variable | | Qualitative by Gender...
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... | | |Statistics | Copyright © 2010, 2006 by University of Phoenix. All rights reserved. Course Description This course surveys descriptive and inferential statistics with an emphasis on practical applications of statistical analysis. The principles of collecting, analyzing, and interpreting data are covered. It examines the role of statistical analysis, statistical terminology, the appropriate use of statistical techniques and interpretation of statistical findings through applications and functions of statistical methods. Policies Faculty and students/learners will be held responsible for understanding and adhering to all policies contained within the following two documents: • University policies: You must be logged into the student website to view this document. • Instructor policies: This document is posted in the Course Materials forum. University policies are subject to change. Be sure to read the policies at the beginning of each class. Policies may be slightly different depending on the modality in which you attend class. If you have recently changed modalities, read the policies governing your current class modality. Course Materials Triola, M. F. (2010). Elementary statistics. (11th ed.). Boston, MA: Pearson. All electronic materials are available...
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...Journal of Economic Literature Vol. XXXIV (March 1996), pp. 97-114 The Standard Error of Regressions By D E I R D R E N . M C C L O S K E Y and STEPHEN T. ZILIAK University of Iowa Suggestions by two anonymous and patient referees greatly improved the paper. Our thanks also to seminars at Clark, Iowa State, Harvard, Houston, Indiana, and Kansas State universities, at Williatns College, and at the universities of Virginia and Iowa. A colleague at Iowa, Calvin Siehert, was materially helpful. T cant for science or policy and yet be insignificant statistically, ignored by the less thoughtful researchers. In the 1930s Jerzy Neyman and Egon S. Pearson, and then more explicitly Abraham Wald, argued that actual investigations should depend on substantive not merely statistical significance. In 1933 Neyman and Pearson wrote of type I and type II errors: HE IDEA OF Statistical significance is old, as old as Cicero writing on forecasts (Cicero, De Divinatione, 1. xiii. 23). In 1773 Laplace used it to test whether comets came from outside the solar system (Elizabeth Scott 1953, p. 20). The first use of the very word "significance" in a statistical context seems to be John Venn's, in 1888, speaking of differences expressed in units of probable error; Is it more serious to convict an innocent man or to acquit a guilty? That will depend on the consequences of the error; is the punishment death or fine; what is the danger to the community of released...
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...Institute of Management Sciences Peshawar Bachelors in Business Studies Course Plan Course Title: Statistics for Business Instructor: Shahid Ali Contact Email shahid.ali@imsciences.edu.pk Semester/Duration: 16 Weeks Course objectives : To introduce students to the concepts of statistics and to equip them with analytical tools to be used in business decision making. The course is intended to polish the numeric ability of the students to identify business problems, describe them numerically and to provide intelligible solutions by data collection and inferential principles. Course pre-requisites Intermediate statistics Attendance Policy: Late arrivals are highly discouraged. Any student coming late to a class late by 5 minutes after the scheduled start time will be marked as absent for the day. The teacher reserves discretion, however, to allow or disallow any student, to sit in the class in case of late arrivals. Attendance is not be entertained once the attendance register is closed. Class Project Students will be divided in groups for a class project. Each group will have to nominate a group leader. The details of the project will be made available to the group leader. Class Presentations Each student will have to make at least one individual presentation and one group presentation in the class. The group presentation will be on the project explained earlier. The individual presentations will...
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...the AIU data set in order to complete a regression analysis for benefits & intrinsic, benefits & extrinsic and benefit and overall job satisfaction. Plus giving an overview of these regressions along with what it would mean to a manager (AIU Online). Introduction Regression analysis can help us predict how the needs of a company are changing and where the greatest need will be. That allows companies to hire employees they need before they are needed so they are not caught in a lurch. Our regression analysis looks at comparing two factors only, an independent variable and dependent variable (Murembya, 2013). Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.018314784 R Square 0.000335431 The portion of the relations explained Adjusted R Square -0.009865228 by the line 0.00033% of relation is Standard Error 1.197079687 Linear. Observations 100 ANOVA df SS MS F Significance F Regression 1 0.04712176 0.047122 0.032883 0.856477174 Residual 98 140.4339782 1.433 Total 99 140.4811 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 4.731133588 1.580971255 2.992549 0.003501 1.593747586 7.86852 Intrinsic -slope 0.055997338 0.308801708 0.181338 0.856477 -0.5568096 0.668804 Line equation is benefits =4.73 + 0.0559 (intrinsic) ...
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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 that...
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...Chapter 1: Introduction – Defining the Role of Statistics in Business • Statistical Analysis: helps extract information from data and provides an indication of the quality of that information • Data mining: combines statistical methods with computer science & optimization in order to help businesses make the best use of the information contained in large data sets • Probability: helps you understand risky and random events and provides a way of evaluating the likelihood of various potential outcomes 1.1 - Why should you learn statistics? o Advertising. Effective? Which Commercial? Which markets? o Quality control. Defect rate? Cost? Are improvements working? o Finance. Risk – how high? How to control? At what cost. o Accounting. Audit to check financial statements. Is error material? o Other – economic forecasting, measuring and controlling productivity 1.2 – What is statistics? • Statistics: the art and science of collecting and understanding data o A complete and careful statistical analysis will summarize the general facts that apply to everyone and will also alert you to any exceptions. 1.3 – The Five Basic Activities of Statistics 1. Design Phase: will resolve these issues so that useful data will result a. Designing the Study involves planning the details of data gathering. Can avoid the costs & disappointment of find out – too late – that the data collected are not adequate to answer the important questions...
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...best result. I have a 1/9 chance or probability to receive an “A” in the data range presented to me which is (A,A-,B,B-,C,C-,D,D- AND F). By the grades that have been posted I would say that the other students have a much better chance of receiving a better grade than mine. I have personally use subjective probability in my security guard business in bidding on contracts based on the clients involved , the rates that I charge versus the rates other companies charge and the amount of work involved to fulfill the agreement. I currently provided security guard services in 11 Asian owned shopping centers and with right elements in place will gain 11 more by utilizing the same pricing model . References EditorialBoard. (2012). Elementary statistics (1st ed.). Words of Wisdom, LLC Subjective probability. (2013). Retrieved from...
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...Unit 5 Regression Analysis American Intercontinental University Regression Analysis Independent Variable: Benefits Dependent Variable: Intrinsic Regression Statistics | | Multiple R | 0.252916544 | R Square | 0.063966778 | Adjusted R Square | 0.045966139 | Standard Error | 0.390066747 | Observations | 54 | ANOVA | | | | | | | df | SS | MS | F | Significance F | Regression | 1 | 0.540685116 | 0.540685116 | 3.553583771 | 0.065010363 | Residual | 52 | 7.911907477 | 0.152152067 | | | Total | 53 | 8.452592593 | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | Intercept | 4.88865703 | 0.188506099 | 25.93368096 | 2.04938E-31 | 4.510391881 | 5.266922187 | 4.510391881 | 5.266922187 | 1.4 | 0.06958624 | 0.036913916 | 1.885095162 | 0.065010363 | -0.004486945 | 0.143659433 | -0.004486945 | 0.143659433 | Independent Variable: Benefits Dependent Variable: Extrinsic Regression Statistics | | Multiple R | 0.332749251 | R Square | 0.110722064 | Adjusted R Square | 0.093620565 | Standard Error | 0.405766266 | Observations | 54 | ANOVA | | | | | | | df | SS | MS | F | Significance F | Regression | 1 | 1.065986925 | 1.065987 | 6.474407048 | 0.013952455 | Residual | 52 | 8.561605668 | 0.164646 | | | Total | 53 | 9.627592593 | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95...
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