Quantitative Methods

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

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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 

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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

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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

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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