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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

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Quantitative Methods

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  1. Quantitative Methods Part 2 Standard Deviation

  2. 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

  3. Standard Deviation • 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

  4. Standard Deviation

  5. 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

  6. 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.

  7. 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 

  8. Can Standard Deviation Help? • His raw score X = 76 • Mean m = 70 • SD 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

  9. Same Student, different module • His raw score X = 76 • Mean m = 70 • SD 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

  10. 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

  11. 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

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