Unit 4-006

# Unit 4-006 - Statistics V3100018.006 UNIT 4 Variability and...

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Statistics – V3100018.006 UNIT 4 – Variability and shape Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1

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2 Analytical instruments A convenient way of summarizing in few “parameters” the characteristics of a frequency distribution.
3 Three characteristics 1. Central tendency 2. Dispersion 3. Shape Mean Median Mode

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Back to our deductive exercise Let us repeat the deductive exercise based on 3 balls drawn from an urn of 4 for the calculation of the median . 4 The mean of all possible sample medians is equal to the true median.
Back to our deductive exercise 5 The highest frequency corresponds to the true value. l Funny z behaviour in the tails.

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Example 1: Weighted mean of grades with different credits Grade Credit Statistics 27 4 Economics 30 8 Maths 24 4 The weighted average 6
7 μ W = w i x i i = 1 N ! w i i = 1 N !

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grade credit grade*credit 27 4 108 30 8 240 24 4 96 mean 27 16 444 weighted mean = =444/16= 27,75 8 Simple mean = 27 Weighted mean = 27.75
9 Water : Price(year 1) = pw1 = 96 Price(year 0) = pw0 = 88 Index: Gold : Price(year 1) = pg1 = 88 Price(year 0) = pg0 = 96 Indice: I w = pw 1 pw 0 ! 100 = 96 88 ! 100 = 109.09 Example 2: Price index I g = pg 1 pg 0 ! 100 = 88 96 ! 100 = 91.66

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