Cognitive Science
1.2.1 The five number summary
1. Min  The smallest score
2. Q1  The first quartile
3. Mdn  The median
4. Q3  The third quartile
5. Max  The largest score
1.2.2 Standard deviation
3 measures of amount of variation in scores (spread):
1. The range, Max  Min
2. The interquartile range, Q3Q1
3. Standard deviation (s)
We discriminate between population standard deviation and sample standard
deviation (that which is based on the whole population, and that which
is based on a sample from the population).
How to find the sample standard deviation (s):
(The example is taken from PSY11PYA PRM Assignment 2, autumn 2001,
La Trobe University)
1. Calculate the sample mean, called X.
This is just the average of all sampled data (the sum of all data divided
by the number of data, n)
For example, if your observed lengths (in centimetres) are:
16.2, 10.4, 7.2, 8.4, 18.4, 12.6, then the sample mean
X = (16.2 + 10.4 + 7.2
+ 8.4 + 18.4 + 12.6) / 6 = 12.2
2. Then find the Sum of Squares, SS:
SS = å
(X  X)^2,
where ^2 means "squared".
{Alternatively, SS = å
(X^2)  [( å
X )^2 / n ] }
Example:
SS = (16.2  12.2)^2 + (10.412.2)^2 + (7.2  12.2)^2 + (8.4  12.2)^2
+ (18.4  12.2)^2 + (12.6  12.2)^2 = 97.28
3. Find s, the sample standard deviation, using the formulae
s^2 = SS / (n1)
Example:
s^2 = 97.28 / 5 = 19.456
s = 4.41
The population standard deviation
The population standard deviation s
= sqrt( SS / N ), where SS = å
(X  m)^2
and N is the number of the population.
The population standard deviation s
can be calculated by the formulae
s^2
= ( å
X^2  Nm^2
) / N
1.2.3 Probability distributions
If we were to conduct an experiment in which the result of each trial
is either success or failure, then the probability of success
P( success ) = ( No. of success outcomes ) / ( Total no. of trials conducted
)
where 0 £
P( success ) £
1. For this number to have any meaning, we have to perform the experiment
a large number of times.
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