Quantitative MethodsQuantitative Methods

Part 2Standard Deviation

Standard DeviationStandard 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 Standard Deviation

To find the standard deviation◦Calculate the deviation from mean (x

– ) ◦Square this (x – ) * (x – )◦Add all squared deviation () = SS◦SD ( ) = Square Root of SS / N

Sigma SD Mu Mean

× Data Value Sum

N Number of data SS = Sum of the Squares

Standard Deviation Standard Deviation

Workshop 3 Activity 4Workshop 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 4Workshop 3 Activity 4Calculate 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 How did I do in my OOP exam?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 Can Standard Deviation Help?Help?

His raw score X = 76 Mean = 70 SD = 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 Same Student, different modulemodule

His raw score X = 76 Mean = 70 SD = 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 - ScoresZ - ScoresZ = ×-μ/σA 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

WorkshopWorkshopWork on Workshop 5 activitiesYour initial Gantt chart and Start

on initial questionsYour journal (Homework)Your Literature Review (Hand in)

ReferencesReferences Dr C. Price’s notes 2010 Gravetter, F. and Wallnau, L. (2003) Statistics for the

Behavioral Sciences, New York: West Publishing Company