UDJ| FINANCE|
Use/Name| Formula| Use/Name| Formula|
Variance (2)(For Poisson, equal to mean)| or n*p*(1-p)| NPV(Costs up front)| | Standard Deviation ()| | Discount Factor| _1_(1+r)n| Exp. Val E(W)of combined linear function| a + bμx + cμxWhere b&c are weights| Annuity Discount Factor| 1-DF or 1-_1_ k ( 1+r)n k| Variance (2)of combined lin funct (X,Y)| b2V(x)+c2V(y)+2bc•Cov(x,y)Where b&c are weights| AnnuityPresent Value| CF X ADF or | Covariance| x y COR(X,Y)| AnnuityFuture Value| |

Correlation (ρ)| | AnnuityPayment| |
Mean| fixi| Growing AnnuityPresent Value| |
Variance Of a Sample (s2)| sqrt to get std dev (s)| PerpetuityPresent Value| CFK| Standard Error(Then to Margin of Error & Confidence Interval)| s/√nwhere s= √x̄(1- x̄)[* (Zɑ/2) for MoE][ ↳ ± x̄ for CI]| Bond Duration| | RequiredSample Size(rework of above)| or | Variance (2)of a portfolio (X,Y)| b2E(x) 2+c2E(y) 2+2bc•Cov(x,y)Where b&c are weights| Confidence IntervalFor a proportion| | SharpeRatio| | Zobs| | Exp. Return of a portfolio| |

Test StatisticZ values Proportions Take this to the table for “P Value”| | βof a portfolio| or | X criticalproportions| Evaluation criteria:| CMLEquation| | | | Cost of Levered Equity| |

| | WACC| |
| | Levered vs. Unlevered Beta| |

μ = x̄ = E(x) Mean| n = number| CF = P = Cashflow or Payment| fi = rel. freq| = Sum of a series| T = time|
xi = middle point| ρ = Correlation| k = r = interest rate| W = combined linear func| = Standard Deviation| g = growth| 2 = Variation| ɑ = E = Margin of Error| rp = Risk of Portfolio| p0 = proportion of hypothesis| β = Beta coeffic. of portfolio| rf = Risk Free Rate|

...of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From...

...compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.
The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.
A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’
In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.
DATA COLLECTION METHODS
Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’...

...Analytical measurement:
measurement uncertainty
and statistics
Ricardo Bettencourt da Silva,
Ewa Bulska, Beata Godlewska-Żyłkiewicz,
Martina Hedrich, Nineta Majcen,
Bertil Magnusson, Snježana Marinčić,
Ioannis Papadakis, Marina Patriarca,
Emilia Vassileva, Philip Taylor
Editors:
Nineta Majcen, Vaidotas Gegevičius
Joint
Research
Centre
Analytical measurement:
measurement uncertainty
and statistics
Editors:
Nineta Majcen
Vaidotas Gegevičius
Authors:
Ricardo Bettencourt da Silva
Ewa Bulska
Beata Godlewska-Żyłkiewicz
Martina Hedrich
Nineta Majcen
Bertil Magnusson
Snježana Marinčić
Ioannis Papadakis
Marina Patriarca
Emilia Vassileva
Philip Taylor
The mission of the JRC is to provide customer-driven scientific and technical support
for the conception, development, implementation and monitoring of EU policies. As
a service of the European Commission, the JRC functions as a reference centre of
science and technology for the Union. Close to the policymaking process, it serves the
common interest of the Member States, while being independent of special interests,
whether private or national.
European Commission
Joint Research Centre
Institute for Reference Materials and Measurements
Contact information
Institute for Reference Materials and Measurements
European Commission
Joint Research Centre
Retieseweg 111
B-2440 Geel
Belgium
E-mail: jrc-irmm-trainmic@ec.europa.eu...

...Department of Decision Sciences
Rational Decision Making
Only study guide for
DSC2602
University of South Africa
Pretoria
c 2010 University of South Africa
All rights reserved.
Printed and published by the
University of South Africa,
Muckleneuk, Pretoria.
DSC2602/1/2011
Cover: Eastern Transvaal, Lowveld (1928) J. H. Pierneef
J. H. Pierneef is one of South Africa’s best known artists.
Permission for the use of this work was kindly granted
by the Schweickerdt family.
The tree structure is a recurring theme in various branches
of the decision sciences.
Preface
Everyday life is full of decisions. What should I wear today? What should I eat? Should I buy
the red or blue shirt? Should I buy a speciﬁc house or buy a piece of land? What is the shortest
route from my house to work? . . . And many more.
Some of these decisions can be made without thinking or by guesswork. Some can be solved by
reasoning or emotions. Some are a bit more diﬃcult and may need additional information.
People have been using mathematical tools to aid decision making for decades. During World
War II many techniques were developed to assists the military in decision making. These developments were so successful that after World War II many companies used similar techniques in
managerial decision making and planning.
The decision making task of...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t like this...

...Statistics 1
Business Statistics
LaSaundra H. – Lancaster
BUS 308 Statistics for Managers
Instructor Nicole Rodieck
3/2/2014
Statistics 2
When we hear about business statistics, when think about the decisions that a manager makes to help make his/her business successful. But do we really know what it takes to run a business on a statistical level? While some may think that business statistics is too much work because it entails a detailed decision making process that includes calculations, I feel that without educating yourself on the processes first you wouldn’t know how to imply statistics. This is a tool managers will need in order to run a successful business. In this paper I will review types of statistical elements like: Descriptive, Inferential, hypothesis development and testing and the evaluation of the results. Also I will discuss what I have learned from business statistics.
My description of Descriptive statistics is that they are the numerical elements that make up a data that can refer to an amount of a categorized description of an item such as the percentage that asks the question, “How many or how much does it take to “ and the outcome numerical amount. According to “Dr. Ashram’s Statistics site” “The quantities most commonly used to measure the...

...Contents
Univariate Data 2
Central tendency 2
Mean 2
Median 3
Mode 3
Trimean 3
Trimmed Mean 3
Spread 3
Range 3
Semi Inter Quartile Rang 3
Variance and Standard Deviation 3
Skew 3
Graphical Representations 4
Frequency Polygons& Cumulative Frequency Polygons 4
Histograms & Bar Graphs 4
Stem and Leaf plots 4
Box Plots 4
Describing Bivariate Data 4
Scatterplots 4
Pearson’s Correlation 4
Spearman’s Rho 4
Probability 4
Binomial Distribution 4
Assumptions: 5
Subjective Probability 5
Normal Distribution 5
Standard Normal Distribution 5
Sampling Distribution 5
Standard Error of Statistic 5
Central Limit Theorem 5
Area under the Sampling Distribution of the Mean 6
Sampling Distribution, Difference between Independent means 6
Sampling Distribution of a Linear Combination of Means 6
Sampling Distribution of Pearson’s R 7
Sampling Distribution of Difference between Independent Pearson’s Rs 7
Sampling Distribution of Median 7
Sampling Distribution of the Standard Deviation 7
Sampling Distribution of a Proportion 7
Correction for Continuity 7
Sampling Distribution of Difference between Two Proportions 7
Point Estimation 7
Characteristics of Estimators 8
Estimating Variance 8
Confidence Intervals 8
CI for Mean, SD Known 8
CI for mean, SD Estimated 8
Genera Formula 8
CI for Difference between means, Independent Groups, SD known 8
CI for Difference between means,...

...Organization of Terms
Experimental Design
Descriptive
Inferential
Population
Parameter
Sample
Random
Bias
Statistic
Types of
Variables
Graphs
Measurement scales
Nominal
Ordinal
Interval
Ratio
Qualitative
Quantitative
Independent
Dependent
Bar Graph
Histogram
Box plot
Scatterplot
Measures of
Center
Spread
Shape
Mean
Median
Mode
Range
Variance
Standard deviation
Skewness
Kurtosis
Tests of
Association
Inference
Correlation
Regression
Slope
y-intercept
Central Limit Theorem
Chi-Square
t-test
Independent samples
Correlated samples
Analysis-of-Variance
Glossary of Terms
Statistics - a set of concepts, rules, and procedures that help us to:
organize numerical information in the form of tables, graphs, and charts;
understand statistical techniques underlying decisions that affect our lives and well-being; and
make informed decisions.
Data - facts, observations, and information that come from investigations.
Measurement data sometimes called quantitative data -- the result of using some instrument to measure something (e.g., test score, weight);
Categorical data also referred to as frequency or qualitative data. Things are grouped according to some common property(ies) and the number of members of the group are recorded (e.g., males/females, vehicle type).
Variable - property of an object or event that can take on different values. ...

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