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Quantitative Methods Part 2 Standard Deviation Standard Deviation Measures the spread of scores within the data set ◦ Population standard deviation is used when you are only interested in your own data ◦ Sample standard deviation is used when you want to generalise for the rest of the population Standard Deviation Sigma s = SD Mu m = Mean × = Data Value S = Sum N = Number of data SS = Sum of the Squares To find the standard deviation ◦ ◦ ◦ ◦ Calculate the deviation from mean (x – m ) Square this (x – m ) * (x – m ) Add all squared deviation (S) = SS SD ( s ) = Square Root of SS / N Standard Deviation Workshop 3 Activity 4 Comp1 and Comp 2 student grades: Comp1: 12, 15, 11, 12, 13, 10, 12, 9, 15, 14, 12, 13 ,14, 11, 12, 13, 14, 11, 13, 11, 10, 12 Comp2: 15, 15, 12, 15, 9, 15, 10, 9, 15, 15, 9, 14, 10, 9, 9, 15, 15, 9, 14, 10, 9, 15 Workshop 3 Activity 4 Calculate the deviation of each number from the mean, like this (data number – mean) (Look at Wk3Act4.xls) Square each of these deviations (data number – mean)*(data number – mean) Add up all these squared deviations. (SS) Calculate the standard deviation as “the square root of (SS divided by N)” where N is the number of data points. How did I do in my OOP exam? A student gets 76 out 100 Sounds good, but is it? Depends on what the rest of the class got ◦ Need to take the mean score into account If mean score = 70 then it is 6 points better than average then But how did the rest of the class do? ◦ Need to know the spread of grades round the mean If lots got 10 points above then Can Standard Deviation Help? His raw score Mean SD X = 76 m = 70 s=3 We can see that the score is 2 sds above average (76 – 70)= 6 and 6/3 = 2 sds • 97.72% got 76 or below • Only 2.28 % did better Same Student, different module His raw score Mean SD X = 76 m = 70 s = 12 We can see that the score is only 1/2 sd above average (76 – 70)= 6 and 6/12 = ½ sd • 69.15% got 76 or below • But 30.85 % did better Z - Scores Z = ×-μ/σ A specific method for describing a specific location within a distribution ◦ Used to determine precise location of an in individual score ◦ Used to compare relative positions of 2 or more scores Workshop Work on Workshop 5 activities Your initial Gantt chart and Start on initial questions Your journal (Homework) Your Literature Review (Hand in) References Dr C. Price’s notes 2010 Gravetter, F. and Wallnau, L. (2003) Statistics for the Behavioral Sciences, New York: West Publishing Company