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Business Statistics Lecture Notes 11

Business Statistics Lecture Notes 11 - MN1025 Business...

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MN1025 – Business Statistics 49 Lecture 11—Not given (revision material) REVISION NOTES References: ‘L’ = Lecture notes Where formulas are given below, you should remem- ber them and know how to use them. 1. Measures of location and dispersion (L1). You should be able to identify these as they are listed in the Descriptive Statistics printout. You need to know how to calculate median, mode and the quar- tiles Q1 and Q3. Variance = (standard deviation) 2 . Suppose a sample is x 1 , x 2 , x 3 , . . . , x n ; the sample size is n . Then sample mean = sample average = ¯ x = 1 n summationdisplay x i ; sample standard deviation = s = radicalbigg ( x i ¯ x ) 2 n 1 ; SE Mean = standard error of the mean = s/ n . 2. Index Numbers (L2). Indexes can be re-based and joined, and you should be able to do that. We have measures, typically of price changes, given by the Laspeyres and the (more expensive but some- times more useful) Paasche index, also the Fisher in- dex, which falls between them, and the Value index. These indexes track changes and can be graphed against time. Laspeyres Price Index = LP = 100 × P t Q 0 P 0 Q 0 . Paasche Price Index = PP = 100 × P t Q t P 0 Q t . Fisher Price Index = LP × PP. Value Index = 100 × P t Q t P 0 Q 0 . 3. Conditional probabilities (L3). What is meant by the probability P ( A | B )? How can you find it? 4. Binomial, Poisson, Normal distributions (L3). When are they used? What are their stan- dard deviations and means? The binomial distribution for n independent trials and probability of success p for each trial is de- noted B ( n, p ). The number of successes in n tri- als has mean μ = np and standard deviation σ = radicalbig np (1 p ). The Poisson distribution (used when p is small and n large) has one parameter = μ = mean = variance. The normal distribution with mean μ and standard deviation σ is denoted N ( μ, σ 2 ). You should be able to sketch it. For the binomial distribution, X can take integer values from X = 0 to X = n . For the Poisson dis- tribution, X can take integer values from X = 0 up- wards. These are discrete probability distributions. The normal distribution is a continuous distribution for which X can take any value, not just integers.
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