• 2 Pages

#### HW_37_38_SOLN

Toledo, ECO 220

Excerpt: ... nship but regression towards the mean Slope = 1: One-to-one relationship; No regression towards the mean (4) Yes. Even if the policy successfully ends strategic studying there will still be regression towards the mean. You should explain why in your own words. (5) (a) y-hat = 0 + 0.712x. The rightmost dashed line (blue) shows that a person with a value of X that is 2 standard deviations above the mean would on average (in expectation) have a value of Y that is about 1.4 standard deviations above the mean. While the conditional expectation E[Y | X = 2] 1.4 is greater than the overall average value of Y (recall Y is standardized so E[Y] = 0), it is not as far above average as X is: 0 < 1.4 < 2. You should finish this explanation yourself by discussing the other two dashed lines. (b) For the first graph where the regression line has a slope of 0.246, a person whose X is two standard deviations above the mean can expect to have a Y that is 0.492 standard deviations above the mean and a person whose X is ...

• 1 Pages

#### section2_7

Georgia Tech, MATH 3070

Excerpt: ... MATH 3070 Introduction to Probability and Statistics Lecture notes Measures of Position Objectives: 1. Understand and use the Empirical Rule The Empirical Rule (68-95-99.7) If the distribution of the data is approximately symmetrical with a single peak we usually refer to this as a normal distribution. The distribution is centered around the mean and has noticeable changes in slope at various points related to the standard deviation. We can say this about the data: 1. 68% of the observations fall within 1 standard deviation of the mean. 2. 95% of the observations fall within 2 standard deviations of the mean. 3. 99.7% of the observations fall within 3 standard deviations of the mean. How can we know this? It depends upon the curve and the characteristics of a symmetrical curve, or density curve. The area underneath the curve is 1 and always positive. The curve bends at each multiple of the standard deviation. These bending points are called inflection points. ...

• 1 Pages

#### 1_Problem_Set

Cornell, PAM 210

Excerpt: ... Book Problem Set #1 Circle all of your final answers. From the book, do: 1.62 (page 49, refers to page 24) Note that the stems are whole percents and the leaves are tenths of a percent so the first number is 5.7. For part b, explicitly list all of th ...

• 1 Pages

#### Lesson - 09

Western Michigan, ECE 380

Excerpt: ... ECE 3800 Lesson Nine - Statistical Computations Special Note: Bring the Lecture Note: Mixed Signal Example to class Vocabulary: Mean Standard Deviation Variance Moments about the origin Moments about the mean Expectation notation Topics: Calculatio ...

• 2 Pages

Western New England College, BIS 220

Excerpt: ... 1. The Standard Normal distribution is a special case of a normal distribution It has a mean and standard deviation of: a. mean=1, standard deviation=0 b. mean=0, standard deviation=1 c. mean=1, standard deviation=1 d. mean=0, standard deviation=0 2. ...

• 3 Pages

#### wi011113

UCLA, STATS 11

Excerpt: ... Statistics 11/Economics 40 Lecture 13 Distribution of the Sample Mean (5.2) 1. Introduction Conceptually, chapter 5.2 says the same things as Chapter 5.1, we are just working with means now instead of counts and proportions. 2. Sampling Distribut ...

• 2 Pages

#### sect2.4

Mercyhurst, M 109

Excerpt: ... Section 2.4: Today we will study How to nd the range of a data set. Measures of Variation How to nd the variance and standard deviation of a population and a sample. How to interpret the standard deviation. Range DEFINITION The range of a data ...

• 6 Pages

#### Exam 2 Review

Arizona, PSYC 230

Excerpt: ... Compare and contrast descriptive statistics and inferential statistics Compare and contrast quantitative data and qualitative data Define and contrast continuous versus discrete variables Be able to identify the independent variable (IV) and the depe ...

• 4 Pages

UCLA, ECON ECON 41

Excerpt: ... UCLA Econ 41 Statistics for Economists Second Quiz, July 23, 20007 Answers Version A: I. Multiple Choice: (5 points each) 1._d_ 2._d_ 3._b_ 4._a_ 5._d_ 6._b_ 7._d_ 8._a_ II. Essay Question (20 points): 1. For distribution A, we have 180 = + (1.0) ...

• 2 Pages

#### s476.c05.stdygd

University of Hawaii - Hilo, UH 476

Excerpt: ... SOCIOLOGY 476/L: Social Statistics University of Hawaii at Mnoa, Spring 2008 Lecture: W 5:30-9:40pm Kuykendall 310 Instructor: Office hours: Quincy Edwards W 7:00pm Computer lab: ONL Saunders Hall 342 Office location: Saunders Hall 247 Email: quincy.edwards@hawaii.edu 5 OVERVIEW OF CHAPTER OBJECTIVES AND STUDY GUIDE CHAPTER 5. MEASURING DISPERSION OR SPREAD IN A DISTRIBUTION OF SCORES. This chapter examines how scores are spread across a distribution and how this spread may be measured. First, we introduce the range, a measure from the lowest to highest score. Second, we introduce the standard deviation, a measure of spread based on how far each score is above or below the mean. In addition, the standard deviation is used to compute standardized scores, a measure of how many standard deviations a score is from the mean. The relationship of the standard deviation and standardized scores to the normal curve is described. The following topics are covered in Chapter 5: 1. Dispersion or spread in a di ...

• 8 Pages

#### STA291_Spring_2009_day_8

Kentucky, ASTRO 11

Excerpt: ... ive square root of the variance s = s2 = (xi x )2 n 1 Standard Deviation: Properties 18 s 0 always s = 0 only when all observations are the same If data is collected for the whole population instead of a sample, then n-1 is replaced by n s is sensitive to outliers 6 2/9/2009 Standard Deviation Interpretation: Empirical Rule 19 If the histogram of the data is approximately symmetric and bell-shaped, then About 68% of the data are within one standard deviation from the mean About 95% of the data are within two standard deviations from the mean About 99.7% of the data are within three standard deviations from the mean Standard Deviation Interpretation: Empirical Rule 20 Sample Statistics, Population Parameters 21 Population mean and population standard deviation are denoted by the Greek letters (mu) and (sigma) They are unknown constants that we would like to estimate ti t Sample mean and sample standard deviation are denoted by x and s ...

• 2 Pages

#### problemset1

Cornell, PAM 2100

Excerpt: ... PAM 2100 Lecture 1 Instructor: Salam Abdus Problem Set #1 Posted: 9th September, 2008. Due: 16th September, Tuesday, 2008, in class, at 1:25 pm Circle all of your final answers. Put your name and your section number at the top. #1) Conservationists have despaired over destruction of tropical rainforest by logging, clearing, and burning. These words begin a report on a statistical study of the effects of logging in Borneo. Researchers compared forest plots that had never been logged (Group 1) with similar plots nearby that had been logged 1 year earlier (Group 2) and 8 years earlier (Group 3). All plots were 0.1 hectare in area. Here are the counts of trees for plots in each group: Group 1 Group 2 Group 3 27 12 18 22 12 4 29 15 22 21 9 15 19 20 18 33 18 19 16 17 22 20 14 12 24 14 12 27 2 28 17 19 19 a) Draw a separate stemplot for each group. b) Calculate the means and standard deviations for Group 1. (Round the mean to two decimal places. Use this number to calculate the standard deviation. ...

• 3 Pages

#### prQuiz6C

Fayetteville State University, MGF 1107

Excerpt: ... This is just a practice quiz; it does not contain all the possible questions that could be asked for these sections. Practice quizzes should just be one component of your studying. As you study you should also use your class notes, study the text sec ...

• 19 Pages

#### Chapter 8 Section 3

San Jacinto, MATH 150

Excerpt: ... .608178 83.66151 260.7148 21 23 14 5 494.6517333 105.9880889 1171.261156 1303.574222 514.5 724.5 539 227.5 ( xi s i 1 x) 2 fi 75 5191.386667 8.37579094 29.35333 n 1 Interpreting the standard deviation 1. The more variation in a data set, the greater the standard deviation. 2. The larger the standard deviation, the more "spread" in the shape of the histogram representing the data. 3. Standard deviation is used for quality control in business and industry. If there is too much variation in the manufacturing of a certain product, the process is out of control and adjustments to the machinery must be made to insure more uniformity in the production process. Three standard deviations rule " Almost all" the data will lie within 3 standard deviations of the mean Mathematically, nearly 100% of the data will fall in the _ _ interval determined by ( x 3s, x 3s) Empirical Rule If a data set is "mound shaped" or "bell-shaped", then: 1. approximat ...

• 4 Pages

#### lec21

BYU, MATH 102

Excerpt: ... points fall within 1 standard deviation of the mean. ii) About 95% of the data points fall within 2 standard deviations of the mean. iii) About 99.7% of the data points fall within 3 standard deviations of the mean. Example 2. If the mean distribution of IQ scores is 100 and the standard deviation is 16, what fraction of people have IQ's between 84 and 116? What fraction have IQ's above 132? 2 Computing Standard Scores Suppose we want to know what fraction of people in the above example have IQ's above 105. We can not do this from the 68-95-99.7 rule. We need the following: Definition 2. The number of standard deviations a data value lies above or below the mean is called its standard score defined by z = standard score = data value - mean standard deviation Example 3. Given the mean of the IQ test to be 100, and the standard deviation to be 16, compute the standard score for an IQ of 105. Definition 3. The nth percentile of a distribution the unique value in the distribution such that n percent of a ...

• 9 Pages

#### # 3

N.C. State, BUS 350

Excerpt: ... es It is often useful to know how many standard deviations a data point x is from the mean. We define z-scores, or standardized scores, as the distance x is from xbar (the mean) in units of the standard deviation. We calculate the z-score for x as follows: z = (x - xbar)/s A z-score of +2 means that an observation is 2 standard deviations above the mean. A z-score of -1.5 means that an observation is 1.5 standard deviations below the mean. End of z-score explanation. Question: Three landmarks of baseball achievement (besides the achievements of Babe Ruth and Henry Aaron) are Ty Cobb's batting average of .420 in 1911, Ted William's .406 in 1941 and George Brett's .390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the decades. The distributions are quite symmetric and (except for outliers such as Cobb, Williams, and Brett) reasonably mound shaped. Although the mean batting average has been held roughly constant by rules ...

• 6 Pages

#### Lecture6

CSU Northridge, MR 31841

Excerpt: ... Lecture 6: Chapter 6: Normal Probability Distributions A normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve. A normal distribution has the following pr ...

• 28 Pages

#### econ41class8_all

UCLA, ECON 41

Excerpt: ... Econ 41 Ekaterini Kyriazidou UCLA Statistics for Economists Class 8: Population and Sampling Distributions In the last lectures we discussed probability distributions of discrete and continuous random variables. The distributions we've seen come ...

• 4 Pages

#### analytical

CSU Fullerton, C 210

Excerpt: ... e from being zero (owing to negative and positive values), we take the average of the squares of the differences and define what is called the standard deviation of a series of measurements Xi: 1 N (X i X )2 N 1 i =1 (note that one divides by N-1 rather than N in order to indicate that the standard deviation is undefined if only one measurement is made). If the probability distribution of our random measurements is normally distributed (e.g., has a Gaussian distribution), the probability of our measurement landing within 1 standard deviation is 68% and within 2 standard deviations is 95.4 %, that is X 68% X 2 95.4% Another important measure of uncertainty is the standard deviation of the mean, X . The standard deviation is the uncertainty in any given measurement, whereas the = standard deviation of the mean is the uncertainty in our best estimate of the true answer using N measurements, that is, the mean X . The standard deviation of the mean is given by X = / N Thus, if our ...

• 2 Pages

#### note

Duke, STA 102

Excerpt: ... Note: Data sets for this chapter are not available; only selected summary measures (means and standard deviations ) were provided in the referenced publications ...

• 2 Pages

#### note

Duke, STA 102

Excerpt: ... Note: Some data sets for this chapter are not available; only selected summary measures (means and standard deviations ) were provided in the referenced publications ...

• 6 Pages

#### NormalPages

UC Davis, IS 8

Excerpt: ... le variance Interpreting the Standard Deviation for Bell-Shaped Curves: The Empirical Rule Once you know the mean and standard deviation for a bell-shaped curve, you can also determine the approximate proportion of the data that will fall into any specied interval. We will learn much more about how to do this in Chapter 8, but for now, here are some useful benchmarks. 44 CHAPTER 2 The Empirical Rule states that for any bell-shaped curve, approximately x 68% 95% of the values fall within 1 standard deviation of the mean in either direction of the values fall within 2 standard deviations of the mean in either direction x x 99.7% of the values fall within 3 standard deviations of the mean in either direction Combining the Empirical Rule with knowledge that bell-shaped variables are symmetric allows the tail ranges to be specied as well. The rst statement of the Empirical Rule implies that about 16% of the values fall more than 1 standard deviation below the mean, and 16% fall more than ...

• 5 Pages

#### 2.5

North Shore, MAT 143

Excerpt: ... Jack-inthe-Box data? Intro to Statistics 3 Measures of Variation Empirical (or 68-95-99.7) Rule for Data with a Bell Shaped Distribution For data sets having a distribution that is approximately bell-shaped, About 68% of all values fall within 1 standard deviation of the mean; About 95% of all values fall within 2 standard deviations of the mean; and About 99.7% of all values fall within 3 standard deviations of the mean. Draw a picture illustrating the empirical rule: Problem(p. 84, #24, 25): Heights of women have a mean of 63.6 in. and a standard deviation of 2.5 in. (based on data from the National Health Survey). Use the range rule of thumb to estimate the minimum and maximum "usual" heights of women. In this context, is it unusual for a woman to be 6 ft tall? Suppose that the heights of women has a bell-shaped distribution. Using the empirical rule, what is the approximate percentage of women whose height is between a. 61.6 in. and 66.1 in.? b. 56.1 in. and 71.1 in.? Intro to ...

• 6 Pages

#### 1-28-09

Allegheny, ECON 203

Excerpt: ... Economic Statistics Class Notes 1/28/09 Recall Continuous Probability Distribution Example The Normal Distribution The Normal Distribution is a distribution described by its mean and standard deviation such that (plus or minus one standard de ...