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Unformatted text preview: Actual vs. Relative Frequency
9 8 7 Frequency 6 5 4 3 2 1 0 2530 3134 3539 4044 Age of participants Actual vs. Relative Frequency
45% 40% Relative Frequency 35% 30% 25% 20% 15% 10% 5% 0% 2530 3134 3539 4044 Age of participants Using a relative frequency distribution chart (e.g. percentage) is often more practical, especially when our data sets start to become much larger. Actual vs. Relative Frequency
Age of participants 4044 15% 2530 25% 3539 40% 3134 20% Some forms of data display are also far more amendable to a relative frequency distribution. Cumulative Frequency Xi 5 6 7 8 9
Mode = 7 Mean = 364/54 = 6.74 f frequency Cumulative frequency Cumulative percentage f x Xi
5x11 = 55 6x13 = 78
7x15 = 105 11 13 15 9 6 11 24 39 48 54 20.37% 44.44% 72.22% 88.88% 100% 8x9 = 72 9x6 = 54
Σ (f x Xi) = 364 From Watt and Van den Berg (1995) p.107 Finding the mode, median mean… But what about the median? Cumulative Frequency Xi 5 6 7 8 9
f frequency Cumulative frequency Cumulative percentage f x Xi
5x11 = 55 6x13 = 78
7x15 = 105 11 13 15 9 6 11 24 39 48 54 20.37% 44.44% 72.22% 88.88% 100% 8x9 = 72 9x6 = 54 From Watt and Van den Berg (1995) p.107 Where would we expect the median to fall? Median = L + N/2 cf f(class) (1) 6.5 + 6.5 + 3 54/2 24 15 6.5 + (1) .2 = 6.7 From Watt and Van den Berg (1995) p.109 15 Brief look at probability Coin flips (the odds of getting heads, 1 out of 2) Deck of cards (the odds of drawing a card with hearts, 13 out of 52 or 1 out of 4)
Probability = Number of events, observations of interest Total number of possible events, observations Coin flips Brief look at probability (the odds of getting heads, 1 out of 2) Well, this is in the context of chance, we are not talking certainty For example, we cannot be sure that the next two tosses of the coin will bring 1 incident of heads Probability – “the relatively frequency of an event over an infinite number of observations…” (Minium, King, Bear, p.217) Fundamental differences with “and”, “or” Deck of cards What are the odds of drawing an ace? 4 out of 52 Brief look at probability What are the odds of drawing the ace of hearts, or the ace of clubs, or the ace of spades, or the ace of diamonds? 1/52 + 1/52 + 1/52 + 1/52 = 4/52 Fundamental differences with “and”, “or” Coin flips Brief look at probability What are the odds of flipping two heads in a row? Now we are concerned with linked outcomes, joint, successive events (“and”) HH, HT, TH, TT ¼, can also be seen as ½ X ½ = ¼ How about 3 H’s in a row? ½ X ½ X ½ = 1/8 This is seen in regard to “independent events…” Meaning, “…the meaning of one event must have no influence on and must in no way be related to the outcome of the other event.”
(Minium et al., p.219) Brief look at probability Anyone knows the gambler’s fallacy? When playing roulette, the gambler keeps track of what numbers have already landed, so that he/she knows when number of “due” to come up… Trouble is, “The wheel has no memory” (Minium et al., p.219) Brief look at probability Binomial distribution – for instances where there are only two possible events P = probability of one event Q = probability of the other event N = number of trials involved (P+Q)N Let’s say P is heads (.5), Q is tails (.5), with 2 coin flips (N) (P+Q)2 = P + 2PQ + Q2
2 2 (.5) + 2(.5)(.5) + (.5)2 Standard normal distribution
.0918 .1359 .0228 .3413 .3413 .1359 .0228 2 1 0 +1 +2
+1.33 Percentage is probability X 100 Percentage of people with higher IQ you, with your IQ is 120, and the mean IQ is 100, with sd of 15 .0918 X 100 = 9.18% ...
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This note was uploaded on 11/05/2009 for the course MGMT 2100 taught by Professor Barryyoung during the Spring '09 term at Rensselaer Polytechnic Institute.
 Spring '09
 BarryYoung

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