Formulae for Final Exam

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School
Humber College **We aren't endorsed by this school
Course
STAT 102
Subject
Statistics
Date
Aug 15, 2023
Pages
4
Uploaded by BarristerSkunk358 on coursehero.com
Formulae for Final Exam A: Chapters (1-3) Measures of Central Tendency The Mean-Arithmetic Average a. The mean of ungrouped data sample mean X = ͞ x n population mean µ = x N b. The Mean of Grouped Data i) For the Population = µ= ∑ fx N Where x = the individual class midpoints f = the number of observations in each class N = ∑ f = the total number of observations in the data set; f x = the sum of the weighted values of the class midpoints ii) For the sample = ´ x = fx n The Median A. The median of ungrouped Data Position number of median in an array = N + 1 2 B. The median Grouped Data Measures of the Variability of Data 1. a) Range
Range = Highest Value - Lowest Value b) Interquartile Range Interquartile range = Q 3 - Q 1 2. Variance a. Ungrouped data Population variance = ϭ 2 = ∑ x µ ¿ ¿ ¿ 2 ¿ ¿ Sample variance = s 2 = ( X ͞͞ X ) ² n 1 = X 2 ( ∑ X ) ² n n 1 3. Standard Deviation a. Ungrouped Data Population Standard Deviation σ = ( x μ ) 2 N Direct Formula for Sample Standard deviation ¿ x 2 ( x ) 2 n n 1 b. Grouped Data Standard Deviation s = f x 2 ( fx ) 2 n n 1 where: x = the midpoint of a class. f = the class frequency. n = is the total number of sample observations Note: Population standard deviation ϭ = ϭ ² Sample standard deviation s = s ²
4. Coefficient of Variation Population coefficient of variation CV = ϭ µ *100 : Sample coefficient of variation CV = s ͞͞ X *100 5. Geometric Mean a) b) For Finding Rate of change from one period to another GM = n Value at end of period Value at the beginningof period B: (Chapters 4-8) 1. Rules of Addition Mutually exclusive - Two events, A and B cannot happen at the same time. a. Special Rule of Addition: P (A or B) = P (A) + P (B) b. General Rule of Addition: P (A or B) = P (A) + P (B) - P (A and B) 2. Rules of Multiplication a. Special Rule of Multiplication - Used for independent events P (A and B) = P (A) * P (B) b. General Rule of Multiplication: Used for dependent events P (A and B) = P (A) P (B|A) 3. Discrete Probability Distribution Expected Value = mean = E (X) = ∑ X.P(X) Variance ( ϭ 2) = ∑ (X - µ) 2 . P(X) Standard Deviation ( ) = ϭ ϭ 2 4. Binomial Probability Distribution Mean and standard deviation of a binomial distribution mean = µ =np standard deviation = = ϭ npq Binomial Formula
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