Measurement of Skewness

Slides:

Advertisements

Similar presentations

Data Analysis Techniques II: Measures of Central Tendencies, Dispersion and Symmetry Advanced Planning Techniques, Lecture 9 Prof. Dr. S. Shabih-ul-Hassan.

Advertisements

Chapter Three McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved

Lecture 2 Describing Data II ©. Summarizing and Describing Data Frequency distribution and the shape of the distribution Frequency distribution and the.

Learning Goal: To be able to describe the general shape of a distribution in terms of its number of modes, skewness, and variation. 4.2 Shapes of Distributions.

Intro to Descriptive Statistics

Review of Basic Statistics. Parameters and Statistics Parameters are characteristics of populations, and are knowable only by taking a census. Statistics.

Review What you have learned in QA 128 Business Statistics I.

Chapter 11 Data Descriptions and Probability Distributions

Standard Scores & Correlation. Review A frequency curve either normal or otherwise is simply a line graph of all frequency of scores earned in a data.

Created by: Tonya Jagoe. Notice The mean is always pulled the farthest into the tail. The median is always in the middle – located between the mean and.

MGQ 201 WEEK 4 VICTORIA LOJACONO. Help Me Solve This Tool.

CHAPTER 3 : DESCRIPTIVE STATISTIC : NUMERICAL MEASURES (STATISTICS)

Statistics. Question Tell whether the following statement is true or false: Nominal measurement is the ranking of objects based on their relative standing.

Copyright © 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins Chapter 16 Descriptive Statistics.

Barnett/Ziegler/Byleen Finite Mathematics 11e1 Learning Objectives for Section 11.2 Measures of Central Tendency The student will be able to calculate.

Slide 1 Lecture 4: Measures of Variation Given a stem –and-leaf plot Be able to find »Mean ( * * )/10=46.7 »Median (50+51)/2=50.5 »mode.

© Copyright McGraw-Hill CHAPTER 3 Data Description.

Topic 1: Descriptive Statistics CEE 11 Spring 2001 Dr. Amelia Regan These notes draw liberally from the class text, Probability and Statistics for Engineering.

Elementary statistics for foresters Lecture 2 Socrates/Erasmus WAU Spring semester 2005/2006.

1 1 Slide Continuous Probability Distributions n A continuous random variable can assume any value in an interval on the real line or in a collection of.

Describing Behavior Chapter 4. Data Analysis Two basic types  Descriptive Summarizes and describes the nature and properties of the data  Inferential.

“STANDARD DEVIATION” Standard Deviation: Std deviation is the best and scientific method of dispersion. It is widely used method used in statistical.

AP Stats Chapter 1 Review. Q1: The midpoint of the data MeanMedianMode.

Probabilistic & Statistical Techniques Eng. Tamer Eshtawi First Semester Eng. Tamer Eshtawi First Semester

Descriptive Statistics

1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach.

Descriptive Statistics The goal of descriptive statistics is to summarize a collection of data in a clear and understandable way.

LECTURE CENTRAL TENDENCIES & DISPERSION POSTGRADUATE METHODOLOGY COURSE.

 Two basic types Descriptive  Describes the nature and properties of the data  Helps to organize and summarize information Inferential  Used in testing.

CHAPTER 3 : DESCRIPTIVE STATISTIC : NUMERICAL MEASURES (STATISTICS)

Chapter SixteenChapter Sixteen. Figure 16.1 Relationship of Frequency Distribution, Hypothesis Testing and Cross-Tabulation to the Previous Chapters and.

2 Kinds of Statistics: 1.Descriptive: listing and summarizing data in a practical and efficient way 2.Inferential: methods used to determine whether data.

By the end of this lesson you will be able to explain/calculate the following: 1. Mean for data in frequency table 2. Mode for data in frequency table.

1 M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 2-4 Measures of Center.

1 a value at the center or middle of a data set Measures of Center.

BASIC STATISTICAL CONCEPTS Chapter Three. CHAPTER OBJECTIVES Scales of Measurement Measures of central tendency (mean, median, mode) Frequency distribution.

1 7.5 CONTINUOUS RANDOM VARIABLES Continuous data occur when the variable of interest can take on anyone of an infinite number of values over some interval.

Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal

Finding averages from the frequency table. In this screencast Mean from frequency table Mean from frequency table with intervals Mode from frequency table.

Educational Research: Competencies for Analysis and Application, 9 th edition. Gay, Mills, & Airasian © 2009 Pearson Education, Inc. All rights reserved.

The following data represent marks of three students’ groups and each group with different teacher, find the mean of each group: A: 59, 61, 62, 58, 60.

Summation Notation, Percentiles and Measures of Central Tendency Overheads 3.

Measures of Central Tendency. Definition Measures of Central Tendency (Mean, Median, Mode)

Bio-Statistic KUEU 3146 & KBEB 3153 Bio-Statistic Data grouping and presentations Part II: Summarizing Data.

Economics 111Lecture 7.2 Quantitative Analysis of Data.

Graphing of data (2) Histograms – Polygon - Ogive.

Summarizing Data with Numerical Values Introduction: to summarize a set of numerical data we used three types of groups can be used to give an idea about.

Properties of Normal Distributions 1- The entire family of normal distribution is differentiated by its mean µ and its standard deviation σ. 2- The highest.

4.3 Probability Distributions of Continuous Random Variables: For any continuous r. v. X, there exists a function f(x), called the density function of.

GROUPED DATA LECTURE 5 OF 6 8.DATA DESCRIPTIVE SUBTOPIC

MATHEMATICS The Measure of Data Location

4.3 Probability Distributions of Continuous Random Variables:

Chapter 5 STATISTICS (PART 1).

Characteristics of the Mean

MEASURES OF CENTRAL TENDENCY

CONTINUOUS PROBABILITY DISTRIBUTIONS CHAPTER 15

Section 2.4 notes continued

Using a histogram to estimate the median

Using a histogram to estimate the median

The Variance How to calculate it.

Probability and Statistics (week-9)

4.3 Probability Distributions of Continuous Random Variables:

Good morning! Please get out your homework for a check.

Statistics 2 Lesson 2.7 Standard Deviation 2.

Educational statistics

13F – skewness.

4.2 Shapes of Distributions

Descriptive statistics for groups:

Presentation transcript:

Measurement of Skewness Unit 4 Measurement of Skewness

Objective : At the end of the course, student should be Able to : i) Define the measurement of skewness ii) Identify the measures of skewness a) Pearson’s Coefficient of Skewness 1 b) Pearson’s Coefficient of Skewness 2 iii) Sketch the data distribution based on the value of PCS 1 and 2

Definition of Measurement of Skewness is a measurement that shows the forms of data distribution and the direction of the frequency distribution; whether skewness to the left, right or symmetrical.

Definition of Measurement of Skewness The concept of skewness helps us to understand the relationship between three measures; mean, median and mode as illustrated below: Mean<Median<Mode Mode<Median<Mean Mean=Median=Mode Mode exceeds Mean and Median. Distribution is Skewed to the left (negative) Mean exceeds Mode and Median. Distribution is Skewed to the right (positive) Distribution is Symmetrical (0)

Definition of Measurement of Skewness There are two formulas to calculate the measurement of skewness :

Definition of Measurement of Skewness Measure of the skewness is use to determine the difference between the mean, median and mode in distribution. The following table can summarize it:

Example 17 : The following table shows the height distribution (cm) for 100 students Height (cm) 151-155 156-160 161-165 166-170 171-175 Frequency 5 20 42 26 7 a) Calculate the: i) Pearson’s Coefficient of Skewness 1 ii) Pearson’s Coefficient of Skewness 2 b) Sketch the distribution’s form based on answers in question (b) c) Give conclusion based on the sketch.

Step 1 : Obtain the midpoint, fx Solution: Step 1 : Obtain the midpoint, fx ( to calculate the mean), cumulative frequency and location of data ( to calculate the median) , x2, fx2( to calculate the variance and standard deviation) in a frequency distribution table.

Step 2 : Find the mean by using the formula : Class Intervals f Mid point, x fx Cumulative Frequency Location of data x2 fx2 151-155 5 153 765 1-5 23409 117045 156-160 20 158 3160 25 6-25 24964 499280 161-165 42 163 6846 67 26-67 26569 1115898 166-170 26 168 4368 93 68-93 28224 733824 171-175 7 173 1211 100 94-100 29929 209503 ∑f= 100 ∑fx= 16350 ∑fx2 = 2675550 Step 2 : Find the mean by using the formula : = 163.5

Step 3 : Identify the location of median class by using the formula : Location of median class = 50

Step 4 : Find the median by using the formula : = 160.5 + 2.98 = 163.48

Step 5 : Identify the mode class (161-165), since this class has the highest frequency = 42 Step 6 : Find the mode by using the formula : = 160.5+ 2.89 = 163.39

Step 7 : Calculate the standard deviation using the formula : = 4.85

Step 8 : Calculate the Pearson’s Coefficient of Skewness 1 by using the formula : = 0.02

Step 9 : Calculate the Pearson’s Coefficient of Skewness 2 using the formula: = 0.01

Step 10 : Sketch the distribution’s form based on answers in Step 9 or 10 Mode<Median<Mean The conclusion is the distribution is skewed to the right or positive skewed

Exercise : 1. The following data was collected from an analysis conducted by a student. a) Find the value of Pearson’s Coefficient of Skewness 1 and 2. b) Determine the type of skewness for the answer in question (a) Average = 64.6 Median = 34.3 Variance = 24432.1 Mode = 35.4