Variance and Standard Deviation (Tables) Lecture 10

Similar documents

Chpt 5. Discrete Probability Distributions. 5-3 Mean, Variance, Standard Deviation, and Expectation

A random variable is a variable whose value is a numerical outcome of a random phenomenon.

Statistics for Business and Economics

Chapter 10 - Lecture 2 The independent two sample t-test and. confidence interval

Statistics for Economics & Business

Lecture 5: Sampling Distribution

ii. Interval estimation:

Combining imperfect data, and an introduction to data assimilation Ross Bannister, NCEO, September 2010

Today: Finish Chapter 9 (Sections 9.6 to 9.8 and 9.9 Lesson 3)

Question 1 (4 points) A restaurant manager is developing a clientele profile. Some of the information for the profile follows:

. (The calculated sample mean is symbolized by x.)

SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 2011

Exam 2. Instructor: Cynthia Rudin TA: Dimitrios Bisias. October 25, 2011

1 Random Variables and Key Statistics

Inferential Statistics and Probability a Holistic Approach. Inference Process. Inference Process. Chapter 8 Slides. Maurice Geraghty,

Sampling Distributions & Estimators

Lecture 5 Point Es/mator and Sampling Distribu/on

These characteristics are expressed in terms of statistical properties which are estimated from the sample data.

ST 305: Exam 2 Fall 2014

Sampling Distributions and Estimation

CHAPTER 8 Estimating with Confidence

Chapter 8. Confidence Interval Estimation. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 8, Slide 1

Topic-7. Large Sample Estimation

Basic formula for confidence intervals. Formulas for estimating population variance Normal Uniform Proportion

A point estimate is the value of a statistic that estimates the value of a parameter.

Further Pure 1 Revision Topic 5: Sums of Series

Correlation possibly the most important and least understood topic in finance

CAPITAL ASSET PRICING MODEL

BASIC STATISTICS ECOE 1323

Fixed Income Securities

I. Measures of Central Tendency: -Allow us to summarize an entire data set with a single value (the midpoint).

Sampling Distributions and Estimation

B = A x z

Introduction to Probability and Statistics Chapter 7

r i = a i + b i f b i = Cov[r i, f] The only parameters to be estimated for this model are a i 's, b i 's, σe 2 i

Estimating Proportions with Confidence

Fixed Income Securities

Standard Deviations for Normal Sampling Distributions are: For proportions For means _

CAPITAL PROJECT SCREENING AND SELECTION

Elementary Statistics and Inference. Elementary Statistics and Inference. Chapter 20 Chance Errors in Sampling (cont.) 22S:025 or 7P:025.

5. Best Unbiased Estimators

Date: Practice Test 6: Compound Interest

CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Means and Proportions

= α e ; x 0. Such a random variable is said to have an exponential distribution, with parameter α. [Here, view X as time-to-failure.

Models of Asset Pricing

FOUNDATION ACTED COURSE (FAC)

We learned: $100 cash today is preferred over $100 a year from now

c. Deaths are uniformly distributed between integer ages. d. The equivalence principle applies.

AY Term 2 Mock Examination

CHAPTER 8 CONFIDENCE INTERVALS

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME

11.7 (TAYLOR SERIES) NAME: SOLUTIONS 31 July 2018

Math 124: Lecture for Week 10 of 17

point estimator a random variable (like P or X) whose values are used to estimate a population parameter

18.S096 Problem Set 5 Fall 2013 Volatility Modeling Due Date: 10/29/2013

Topic 14: Maximum Likelihood Estimation

c. Deaths are uniformly distributed between integer ages. d. The equivalence principle applies.

Hopscotch and Explicit difference method for solving Black-Scholes PDE

x satisfying all regularity conditions. Then

Chapter 5 Discrete Probability Distributions. Random Variables Discrete Probability Distributions Expected Value and Variance

DOWLING COLLEGE: School of Education Department of Educational Administration, Leadership, and Technology

Discrete Probability Distribution

Lecture 18 Section Mon, Feb 16, 2009

Models of Asset Pricing

Models of Asset Pricing

Lecture 18 Section Mon, Sep 29, 2008

Online appendices from The xva Challenge by Jon Gregory. APPENDIX 10A: Exposure and swaption analogy.

NOTES ON ESTIMATION AND CONFIDENCE INTERVALS. 1. Estimation

Random Variables. Discrete Random Variables. Example of a random variable. We will look at: Nitrous Oxide Example. Nitrous Oxide Example

CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Means and Proportions

Quantitative Analysis

2-4 Completing the Square

Lecture 4: Probability (continued)

A) 0.74 B) 2.96 C) 8.89 D) 0.92

Name Date MATH REVIEW 2. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

CAUCHY'S FORMULA AND EIGENVAULES (PRINCIPAL STRESSES) IN 3-D

Parameter Uncertainty in Loss Ratio Distributions and its Implications

Solutions to Problem Sheet 1

Creating a Rolling Income Statement

1. Suppose X is a variable that follows the normal distribution with known standard deviation σ = 0.3 but unknown mean µ.

Section 3.3 Exercises Part A Simplify the following. 1. (3m 2 ) 5 2. x 7 x 11

Dr. Maddah ENMG 624 Financial Eng g I 03/22/06. Chapter 6 Mean-Variance Portfolio Theory

Section 1.5: Factoring Special Products

ISBN Copyright 2015 The Continental Press, Inc.

14.30 Introduction to Statistical Methods in Economics Spring 2009

Standard BAL a Real Power Balancing Control Performance

Lecture 4: Parameter Estimation and Confidence Intervals. GENOME 560 Doug Fowler, GS

Commonly Used Technical Indicators

Appendix 1 to Chapter 5

Parametric Density Estimation: Maximum Likelihood Estimation

1. Find the area under the standard normal curve between z = 0 and z = 3. (a) (b) (c) (d)

Chapter 17. The. Value Example. The Standard Error. Example The Short Cut. Classifying and Counting. Chapter 17. The.

of Asset Pricing R e = expected return

Chapter 17 Sampling Distribution Models

of Asset Pricing APPENDIX 1 TO CHAPTER EXPECTED RETURN APPLICATION Expected Return

Summary. Recap. Last Lecture. .1 If you know MLE of θ, can you also know MLE of τ(θ) for any function τ?

Single-Payment Factors (P/F, F/P) Single-Payment Factors (P/F, F/P) Single-Payment Factors (P/F, F/P)

The Likelihood Ratio Test

Transcription:

Variace ad Stadard Deviatio (Tables) Lecture 10

Variace ad Stadard Deviatio Theory I this lesso: 1. Calculatig stadard deviatio with ugrouped data.. Calculatig stadard deviatio with grouped data. What you should be able to do: 1. Calculate stadard deviatio of tables with group or ugrouped data.

Calculatig Stadard Deviatio with ugrouped data Whe calculatig stadard deviatio with frequecy tables, always use the followig formula: Ugrouped data σ = Σfx i Σfx i Add the colums: fx, fx, ad the row: total. The big differeces betwee calculatig with ugrouped data ad lists is that you must multiply by the frequecy.

Calculatig Stadard Deviatio with ugrouped data Whe calculatig stadard deviatio with frequecy tables, always use the followig formula: Ugrouped data σ = Σfx i Σfx i Add the colums: fx, fx, ad the row: total. Step : Fill out the ew table. Step 3: Put the umbers from the total row ito the correct parts of the formula Step 4: Subtract the two umbers Step 5: Take the square root of the variace to fid the stadard deviatio Σfx i Σfx i The big differeces betwee calculatig with ugrouped data ad lists is that you must multiply by the frequecy.

Calculatig Stadard Deviatio with ugrouped data Whe calculatig stadard deviatio with frequecy tables, always use the followig formula: Ugrouped data Σfx i Σfx i σ = 154, 050 109 σ = Σfx i Σfx i 4, 096 109 σ 1. 198 studets σ = 154, 050 109 σ 1. 09 studets 4, 096 109 The big differeces betwee calculatig with ugrouped data ad lists is that you must multiply by the frequecy. Add the colums: fx, fx, ad the row: total. Step : Fill out the ew table. Step 3: Put the umbers from the total row ito the correct parts of the formula Step 4: Subtract the two umbers Step 5: Take the square root of the variace to fid the stadard deviatio

Calculatig Stadard Deviatio with ugrouped data Whe calculatig stadard deviatio with frequecy tables, always use the followig formula: Grouped data σ = Σfx i Σfx i Add the colums: midpoit x, fx, fx, ad the row: total. The big differeces betwee calculatig with grouped data ad ugrouped data is that you must fid the midpoit of each row.

Calculatig Stadard Deviatio with ugrouped data Whe calculatig stadard deviatio with frequecy tables, always use the followig formula: Grouped data σ = Σfx i Σfx i Add the colums: midpoit x, fx, fx, ad the row: total. Step : Fill out the ew table. Step 3: Put the umbers from the total row ito the correct parts of the formula Step 4: Subtract the two umbers Step 5: Take the square root of the variace to fid the stadard deviatio x Σfx i Σfx i The big differeces betwee calculatig with grouped data ad ugrouped data is that you must fid the midpoit of each row.

Calculatig Stadard Deviatio with ugrouped data Whe calculatig stadard deviatio with frequecy tables, always use the followig formula: Grouped data x Σfx i Σfx i σ = σ = Σfx i 6, 487. 5 7 σ 18. 858 mi σ = 6, 487. 5 7 σ 11. 35 mi Σfx i 85 7 85 7 Add the colums: midpoit x, fx, fx, ad the row: total. Step : Fill out the ew table. Step 3: Put the umbers from the total row ito the correct parts of the formula Step 4: Subtract the two umbers Step 5: Take the square root of the variace to fid the stadard deviatio The big differeces betwee calculatig with grouped data ad ugrouped data is that you must fid the midpoit of each row.