# Unit 3 - Statistics V3100018.001 UNIT 3 Analytical...

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Statistics – V3100018.001 UNIT 3 – Analytical synthesis Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1

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Analytical tools A convenient way to summarize in few “ parameters ” the main features of frequency distributions 2
A frequency distribution displays three main features Central tendency Dispersion Distribution 3

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Central tendency Refers to the position of the frequency distribution in the graph. It is measured by: - Mean - Median - Mode 4
5 Sum of all values divided by the number of individuals: μ= x 1 + x 2 + ... + x i + ... + x n " 1 + x n ( ) n = x i i = 1 n # n It can be computed only for Quantitative variables The (arithmetic) mean

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6 Example: The mean of the returns of 17 financial assetts: 32,2 29,5 29,9 32,4 30,5 30,1 32,1 35,2 10 20,6 28,6 30,5 38 33 29,4 37,1 28,6 86 , 29 17 6 , 28 ... 9 , 29 5 , 29 2 , 32 = + + + + = μ
7 The mean is the equilibrium point of a distribution

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8 Let us define the difference ( ) μ ε = i i x i = 1, 2, …, n " i i = 1 n # = 0 The mean satisfies the property:
9 The mean is invariant to linear transformations: Given the distribution x 1 , x 2 ,..., x n ; μ X Defining a new variable y 1 , y 2 ,..., y n such that i i bx a y + = Its mean will be X Y b a + = .

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