Psyc_315_-_Winter_2010_-_Class_5

# Psyc_315_-_Winter_2010_-_Class_5 - Recap of Last Class...

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1 Recap of Last Class • Measures of Central Tendency – The Mean – The Mode – The Median – Variance • Questions? Chapter 5 Standard deviation and Z-scores 3 Problem • A spread measure should have the same units as the original data. • E.g., weight of students - variance would be lbs squared. • Also, difficult to interpret the actual spread of the scores (e.g., variance of 1000 does not give insight into actual variation of weights). • The solution is to take the square root – The Standard Deviation.

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4 Measures of Variability: The Standard Deviation • The standard deviation (SD) is the square root of the variance (averaged squared deviation from the mean). • The standard deviation tells us approximately how far the scores vary from the mean on average. • The value of the SD is that it permits a measure of relative standing within a distribution of scores. • The bigger the standard deviation, the greater the spread 2 S D S D = 5 Measures of Variability: The Standard Deviation Definitional Formula: • Step 1 : Find X. • Step 2 : Subtract the mean from each score. • Step 3 : Square each deviation (X - M). • Step 4 : Sum the squared deviations (X - M) 2 to obtain SS. • Step 5 : Enter SS and N in formula below to obtain SD. 2 2 ( ) X M SS SD SD N N - = = = 6 Measures of Variability: The Standard Deviation Computational Formula: • Get the same answer with either formula. • The major difference is how SS is calculated. • Computing SS using the computational formula: – Step 1 : Square each score – Step 2 : Calculate Σ X 2 (sum the squared scores) – Step 3 : Calculate Σ X (sum of scores) and square it ( Σ X) 2 – Step 4 : Calculate SS using the formula. – Step 5: Enter SS and N in SD formula. ( ) 2 2 X SS X N = - SS SD N =
7 Example Using Definitional Formula X = [75,70,80,40,60,85,75,90,70,55] M= X = 700 = 70 N 10 SS = (X - M) 2 = 2000 SD 2 = SS = 2000 = 200 N 10 SD = SD 2 = 200 = 14.14 Scores vary, on average, by about 14.14 in each direction from the mean (55.86 – 84.14). X X-M (X - M) 2 75 5 25 70 0 0 80 10 100 40 -30 900 60 -10 100 85 15 225 75 5 25 90 20 400 70 0 0 55 -15 225 8 Example Using Computational Formula X = [75,70,80,40,60,85,75,90,70,55] SS = X 2 – ( X) 2 = 51000 – (700) 2 = 2000 N 10 SD 2 = SS = 2000 = 200 N 10 SD= SD 2 = 200 = 14.14 X X 2 75 5625 70 4900 80 6400 40 1600 60 3600 85 7225 75 5625 90 8100 70 4900 55 3025 9 Your Turn Calculate the Mean (M), Variance (SD 2 ) and Standard Deviation (SD) of these 2 sets of numbers: a) X= [1,2,3,5,7,9] b) X= [22, 33, 44, 88] M= X N SS = (X - M) 2 SD 2 = SS N SD = SD 2

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10 11 Answers X (X-M) (X-M) 2 1 -3.5 12.25 2 -2.5 6.25 3 -1.5 2.25 5 0.5 0.25 7 2.5 6.25 9 4.5 20.25 2 2 4.5 47.5 47.5 7.92 6 7.92 2.81 M SS SS SD N SD SD = = = = = = = = X (X-M) (X-M) 2 22 -24.75 612.56 33 -13.75 189.06 44 -2.75 7.56 88 41.25 1701.56 2 2 46.75 2510.75 2510.75 627.69 4 627.69 25.05 M SS SS SD N SD SD = = = = = = = = 12 An important note about the standard
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## This note was uploaded on 04/29/2010 for the course PSYCH 315 taught by Professor Afroditipanagopoulos during the Winter '10 term at Concordia Canada.

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Psyc_315_-_Winter_2010_-_Class_5 - Recap of Last Class...

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