2011-Psych 60-Lecture 5

2011-Psych 60-Lecture 5 - 4/6/11 Announcements Homework 1...

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Unformatted text preview: 4/6/11 Announcements Homework 1 Answer Key available on WebCT Homework 1 scores will be available later today Announcements Homework 1 Answer Key available on WebCT Homework 1 scores will be available later today hFp://office.microso@.com/en-us/web-apps/ Free Microso@ Excel in the "cloud" 1 4/6/11 hFp://office.microso@.com/en-us/web-apps/ hFp://office.microso@.com/en-us/web-apps/ hFp://office.microso@.com/en-us/web-apps/ hFp://office.microso@.com/en-us/web-apps/ 2 4/6/11 hFp://office.microso@.com/en-us/web-apps/ hFp://office.microso@.com/en-us/web-apps/ hFp://office.microso@.com/en-us/web-apps/ hFp://office.microso@.com/en-us/web-apps/ 3 4/6/11 hFp://office.microso@.com/en-us/web-apps/ Last Time FR O FO BE M RE Bar Chart Line Chart Frequency DistribuPons Clicker IntroducPon and Try-out Visual Displays of Data ScaFer plots 4 4/6/11 FR O FO BE M RE FR O FO BE M RE Frequency DistribuPon Table Frequency DistribuPons Types of Frequency Frequency DistribuPons DistribuPons Frequency DistribuPon Graph Grouped Frequency DistribuPon Table Grouped Frequency DistribuPon Graph FR O FO BE M RE FR O FO BE M RE Frequency DistribuPon Table Cups 4 3 2 1 0 f 2 2 3 2 1 p .20 .20 .30 .20 .10 Cups of Coffee Consumed Each Day N = 10 Individuals 2, 4, 3, 4, 2, 3, 1, 0, 2, 1 5 4/6/11 FR O FO BE M RE Frequency DistribuPon Graph 4 3 FR O FO BE M RE Frequency DistribuPon Graph 4 3 f 2 1 0 0 1 2 3 4 f 2 1 0 0 1 2 3 4 Cups of Coffee Cups of Coffee FR O FO BE M RE Frequency DistribuPon Graph 4 3 FR O FO BE M RE Frequency DistribuPon Graph 4 3 f 2 1 f Ryan 2 Jon 1 Ryan 0 1 2 3 4 0 1 2 3 4 0 0 Cups of Coffee Cups of Coffee 6 4/6/11 FR O FO BE M RE FR O FO BE M RE Popula'on of ci'es in thousands N = 100 ci'es Grouped Frequency DistribuPon Table Pop. f 4000-4399 3600-3999 3200-3599 2800-3199 2400-2799 2000-2399 1600-1999 1200-1599 800-1199 400-799 0 - 399 1 0 1 0 0 2 6 16 41 19 14 220, 430, 301, 40, 290, 3000, 1230, 647, 356, 910, 22, 37, 483, 273, 84, 912, 378, 374, 12, 0.4, 2, 121, 54, 72, 145, 8, 376, 5, 981, 43, 777, 35, 427, 35, 467, 19, 23, 456, 37, 45, 366, 298... FR O FO BE M RE Grouped Frequency DistribuPon Graph 45 40 35 30 25 20 15 10 5 0 0 - 3 40 99 0- 80 799 0- 12 119 00 9 - 16 159 00 9 - 20 199 00 9 - 24 239 00 9 - 28 279 00 9 - 32 319 00 9 - 36 359 00 9 - 40 399 00 9 -4 39 9 This Week f Visual Displays of Data Measures of Central Tendency Measures of Variability PopulaPon of City (thousands) 7 4/6/11 Describing Distribu5ons Today Describing Distribu5ons Today Shape Central Tendency Shape Central Tendency Describing the Shape of DistribuPons Describing the Shape of DistribuPons Symmetry 8 4/6/11 Symmetry 4 Frequency DistribuPon Graph A distribuPon is symmetric if one side of the distribuPon can be exactly reflected on to the other (across an axis of symmetry) 3 f 2 1 0 0 1 2 3 4 Cups of Coffee Frequency DistribuPon Graph 4 3 4 3 Frequency DistribuPon Graph f 2 1 0 0 1 2 3 4 f 2 1 0 0 1 2 3 4 Cups of Coffee Cups of Coffee 9 f 0 1 2 3 45 40 35 30 25 20 15 10 5 0 0 1 2 3 f 4 Cups of Coffee Frequency DistribuPon Graph Grouped Frequency DistribuPon Graph PopulaPon of City (thousands) 4 0 - 3 40 99 0- 80 799 0- 12 119 00 9 - 16 159 00 9 - 20 199 00 9 - 24 239 00 9 - 28 279 00 9 - 32 319 00 9 - 36 359 00 9 - 40 399 00 9 -4 39 9 f 45 40 35 30 25 20 15 10 5 0 f 45 40 35 30 25 20 15 10 5 0 Grouped Frequency DistribuPon Graph Grouped Frequency DistribuPon Graph PopulaPon of City (thousands) PopulaPon of City (thousands) 0 - 3 40 99 0- 80 799 0- 12 119 00 9 - 16 159 00 9 - 20 199 00 9 - 24 239 00 9 - 28 279 00 9 - 32 319 00 9 - 36 359 00 9 - 40 399 00 9 -4 39 9 0 - 3 40 99 0- 80 799 0- 12 119 00 9 - 16 159 00 9 - 20 199 00 9 - 24 239 00 9 - 28 279 00 9 - 32 319 00 9 - 36 359 00 9 - 40 399 00 9 -4 39 9 4/6/11 10 f 45 40 35 30 25 20 15 10 5 0 Grouped Frequency DistribuPon Graph PopulaPon of City (thousands) 0 - 3 40 99 0- 80 799 0- 12 119 00 9 - 16 159 00 9 - 20 199 00 9 - 24 239 00 9 - 28 279 00 9 - 32 319 00 9 - 36 359 00 9 - 40 399 00 9 -4 39 9 4/6/11 11 4/6/11 Describing the Shape of DistribuPons Symmetry Describing the Shape of DistribuPons Symmetry Symmetric Asymmetric Describing the Shape of DistribuPons Symmetry Symmetric Asymmetric PosiPve Skew "tail" dragged off to the right Skew 12 4/6/11 PosiPve Skew "tail" dragged off to the right PosiPve Skew "tail" dragged off to the right NegaPve Skew "tail" dragged off to the le@ 13 4/6/11 NegaPve Skew "tail" dragged off to the le@ NegaPve Skew "tail" dragged off to the le@ Describing the Shape of DistribuPons Symmetry Symmetric Asymmetric Skew 14 4/6/11 Describing the Shape of DistribuPons Symmetry Symmetric Asymmetric Check Your Understanding Skew PosiPve Skew (skewed to the right) NegaPve Skew (skewed to the le@) This distribuPon is: A B PosiPvely Skewed (Skewed to the right) NegaPvely Skewed (Skewed to the le@) Check Your Understanding Describing Distribu5ons Today Shape Central Tendency This distribuPon is: A B PosiPvely Skewed (Skewed to the right) NegaPvely Skewed (Skewed to the le@) 15 4/6/11 Describing Distribu5ons Today Central Tendency A measure of central tendency is a number that represents the middle of a distribuPon Shape Central Tendency Click In Your Opinion! Where is the middle? Where is the middle? A B C D E 16 4/6/11 Click In Your Opinion! Where is the middle? Typical Measures of Central Tendency Mean Median Mode A B C D Typical Measures of Central Tendency The Mean The mean is the sum of a set of scores divided by the number of scores in the set Mean Median Mode Commonly known as the "average" Appropriate for interval, or raPo scale data Not valid for nominal or ordinal scale data 17 4/6/11 FR FO BE OM RE "PopulaPon" A populaPon is the set of all individuals (units) of interest FR O FO BE M RE "Sample" A sample is a set of individuals (units) selected from a populaPon Plankton in the ocean, People in the world, People at UCSD, Dogs in San Diego Usually intended to "represent" the populaPon Usually much smaller than populaPon FR BE OM FO RE Parameters and StaPsPcs Parameter: a value (usually numeric) that describes a populaPon StaPsPc: a value (usually numeric) that describes a sample The Mean The mean is the sum of a set of scores divided by the number of scores in the set Commonly known as the "average" Appropriate for interval, or raPo scale data Not valid for nominal or ordinal scale data 18 4/6/11 PopulaPon Sample CalculaPng the Mean - PopulaPon Formula - "mew" M "M" X "X bar" Sum o = Number f oSf cores Scores CalculaPng the Mean - PopulaPon Formula - CalculaPng the Mean - PopulaPon Formula - !X = N !X = N 19 4/6/11 SummaPon NotaPon !X ! Take the sum of X 8 6 7 9 i X 8 6 7 9 1 2 3 4 20 4/6/11 i Index Number X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !X ? !X = 8 + 6 + 7 + 9 21 4/6/11 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !X = 30 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !Xi !Xi = X1 + X2 + X 3 + X 4 22 4/6/11 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !Xi = 8 + 6 + 7 + 9 !Xi = 30 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !(Xi2 )? 23 4/6/11 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 2 2 2 !(Xi2 ) = X12 + X2 + X 3 + X 4 !(Xi2 ) = 8 2 + 6 2 + 7 2 + 9 2 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !(Xi2 ) = 64 + 36 + 49 + 81 !(Xi2 ) = 230 24 4/6/11 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 (!Xi )2 ? i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 (!Xi )2 = (X1 + X2 + X 3 + X 4 )2 (!Xi )2 = (8 + 6 + 7 + 9)2 25 4/6/11 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 (!Xi )2 = (30)2 (!Xi )2 = 900 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !(Xi2 ) = 230 (!Xi )2 = 900 26 4/6/11 i X 8 6 7 9 i X 8 6 7 9 1 2 3 4 1 2 3 4 !Xi " # Xi i =1 4 !Xi " # Xi i =1 4 i X 8 6 7 9 1 2 3 4 Check Your Understanding i Find !(Xi + 2) 4 X 0 3 8 3 1 2 3 4 !Xi " # Xi i =1 A B C D E 20 16 22 14 Huh? 27 4/6/11 Check Your Understanding i Find !(Xi + 2) A B C D E 20 16 22 14 Huh? X 0 3 8 3 i 1 2 3 4 Find !(Xi + 2) X 0 3 8 3 1 2 3 4 i X 0 3 8 3 i X 0 3 8 3 Find !(Xi + 2) 1 2 3 4 Find !(Xi + 2) (X1 + 2) + (X2 + 2) + (X 3 + 2) + (X 4 + 2) 1 2 3 4 28 4/6/11 i X 0 3 8 3 i X 0 3 8 3 Find !(Xi + 2) (X1 + 2) + (X2 + 2) + (X 3 + 2) + (X 4 + 2) (0 + 2) + (3 + 2) + (8 + 2) + (3 + 2) 1 2 3 4 Find !(Xi + 2) (X1 + 2) + (X2 + 2) + (X 3 + 2) + (X 4 + 2) (0 + 2) + (3 + 2) + (8 + 2) + (3 + 2) (2) + (5) + (10) + (5) 1 2 3 4 i X 0 3 8 3 Find !(Xi + 2) (X1 + 2) + (X2 + 2) + (X 3 + 2) + (X 4 + 2) (0 + 2) + (3 + 2) + (8 + 2) + (3 + 2) (2) + (5) + (10) + (5) 22 1 2 3 4 SummaPon NotaPon ! Take the sum of 29 4/6/11 CalculaPng the Mean - PopulaPon Formula - !X !X = N CalculaPng the Mean - PopulaPon Formula - CalculaPng the Mean - PopulaPon Formula - !X = N !Xi = N 30 4/6/11 CalculaPng the Mean - Sample Formula - PopulaPon Sample !Xi X= n !Xi = N !Xi X= n Visualizing the Mean 31 4/6/11 -3 -3 -3 32 4/6/11 -3 -3 +1 -3 -3 +1 +5 -3 -3 +1 +5 (-3) + (-3) + (1) + (5) = 0 33 4/6/11 4 3 Check Your Understanding Find the mean of the following: 2, 4, 3, 4, 2, 3, 1, 0, 2, 1 A B C D E 2 2.2 3.2 10 22 f 2 1 0 0 1 2 3 4 Check Your Understanding Find the mean of the following: 2, 4, 3, 4, 2, 3, 1, 0, 2, 1 ... Xi = 22 A B C D E 2 2.2 3.2 10 22 Check Your Understanding Find the mean of the following: 2, 4, 3, 4, 2, 3, 1, 0, 2, 1 ... Xi = 22 A B C D E 2 2.2 3.2 10 22 34 4/6/11 4 3 Typical Measures of Central Tendency f 2 1 0 0 1 2 3 4 Mean Median Mode Typical Measures of Central Tendency The Median The median is the score that divides a distribuPon so that 50% of individuals are at or below that value Mean Median Mode Appropriate for ordinal, interval, or raPo scale data Not valid for nominal data 35 4/6/11 Median for odd number of scores 8 5 8 1 6 CalculaPng the Median for an odd number of scores 1. Order scores from lowest to highest 8 5 8 1 6 36 4/6/11 CalculaPng the Median for an odd number of scores 1 5 6 8 8 1. Order scores from lowest to highest 2. Median = number halfway in; i = (N+1)/2 i = (N+1)/2 = i = (N+1)/2 = (5+1)/2 = 1 5 6 8 8 1 5 6 8 8 37 4/6/11 i = (N+1)/2 = (5+1)/2 = 6/2 = i = (N+1)/2 = (5+1)/2 = 6/2 = 3 1 5 6 8 8 1 5 6 8 8 i = (N+1)/2 = (5+1)/2 = 6/2 = 3 i = (N+1)/2 = (5+1)/2 = 6/2 = 3 1 5 6 8 8 1 5 6 8 8 38 4/6/11 i = (N+1)/2 = (5+1)/2 = 6/2 = 3 Median 1 5 6 8 8 6 CalculaPng the Median for an odd number of scores 1. Order scores from lowest to highest 2. Median = number halfway in; i = (N+1)/2 CalculaPng the Median for an odd number of scores 1. Order scores from lowest to highest 2. Median = Xi , where i = (N+1)/2 39 4/6/11 CalculaPng the Median for an even number of scores Median for even number of scores 1. Order scores from lowest to highest CalculaPng the Median for an even number of scores 1. Order scores from lowest to highest 2. Median = mean of the two numbers halfway in: i=N/2, and i=(N/2)+1 1 5 6 8 8 11 40 4/6/11 N/2 = N/2 = 6/2 = 1 5 6 8 8 11 1 5 6 8 8 11 N/2 = 6/2 = 3 N/2 = 6/2 = 3 (N/2)+1 = 1 5 6 8 8 11 1 5 6 8 8 11 41 4/6/11 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 1 5 6 8 8 11 1 5 6 8 8 11 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 1 5 6 8 8 11 1 5 6 8 8 11 42 4/6/11 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 1 5 6 8 8 11 1 5 6 8 8 11 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 1 5 6 8 8 11 1 5 6 8 8 11 43 4/6/11 N/2 = 6/2 = 3 (N/2)+1 = (6/2)+1 = 3+1 = 4 1 5 6 8 8 11 6 8 6 8 2 6 8 2 7 44 4/6/11 Median 7 CalculaPng the Median for an even number of scores 1. Order scores from lowest to highest 2. Median = mean of the two numbers halfway in: i=N/2, and i=(N/2)+1 CalculaPng the Median for an even number of scores 1. Order scores from lowest to highest 2. Median = (Xi + Xi+1)/2 where i = N/2 45 4/6/11 Check Your Understanding Find the median of the following: 4, 20, 2, 8, 6 A B C D E 8 4 2 40 6 Check Your Understanding Find the median of the following: 4, 20, 2, 8, 6 Typical Measures of Central Tendency Mean Median Mode A B C D E 8 4 2 40 6 46 4/6/11 Typical Measures of Central Tendency The Mode The mode is the score or category that has the greatest frequency Mean Median Mode Appropriate for nominal, ordinal, interval, or raPo scale data 1 5 6 8 8 11 1 5 6 8 8 11 47 4/6/11 4 3 4 3 f 2 1 0 0 1 2 3 4 f 2 1 0 0 1 2 3 4 48 4/6/11 Pets my Friends Have Bimodal DistribuPon Pets my Friends Have 49 4/6/11 When to Use Each Measure Mean 1. When data are interval/raPo scale 2. Use unless there is a substanPal reason not to Median 1. When Data are ordinal 2. When interval/ raPo data is highly skewed or there are extreme scores (outliers) Mode When to Use Each Measure Mean 1. When data are interval/raPo scale 2. Use unless there is a substanPal reason not to Median 1. When Data are ordinal 2. When interval/ raPo data is highly skewed or there are extreme scores (outliers) Mode 1. When data are nominal. 2. When most common score is the most meaningful way to describe the data Median Mode Mean 50 4/6/11 For Next Time Read: Ch. 4 Review answers to Homework 1 Try out Excel online 51 ...
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This note was uploaded on 01/10/2012 for the course PSYC PSYC 60 taught by Professor ? during the Winter '09 term at UCSD.

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