Quantitative Methods

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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
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