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1 ••• Master List of Formulas Chapter 1 IntroduCtIon and desCrIptIve statIstICs NONE. Chapter 2 FrequenCy dIstrIbutIons In tables and Graphs Σx (Frequency) Σx n (Relative frequency) Σx n × 100 (Relative percent) Chapter 3 summarIzInG data: Center tendenCy µ= Σx N (Population mean) M = Σx n (Sample mean) M Mn w n = Σ × Σ (Weighted sample mean) Chapter 4 summarIzInG data: varIabIlIty
For a discrete random variable X taking values xi with probabilities pi Expectation (mean): E(X) = μ = Σ xi pi Variance: Var(X) = σ2 = Σ(xi − μ)2 pi = Σ x 2. i pi − μ2. For a function g(X) : E(g(X)) = Σ g(xi) pi. The probability generating function (P.G.F.) of X is GX (t) = E(tX), and E(X) = GX ′ (1), Var(X) = G ′′. (1) + G
2 Chapter 3 sample size population size frequency n N f sum w weight = = = Σ= = Sample mean: Population mean: () Weighted mean: Mean for frequency table: highest value + lowest value Midrange 2 x x n x N wx x w f x x f µ ∑ = ∑ = ∑• = ∑ ∑• = ∑ = 2 2 2 2 Range = Highest value - Lowest value Sample standard deviation: 1 ...
2 Test Statistic. 2 is a generally accepted variable4 which can test the “goodness-of-fit,” i.e. agreement between theory and experiment. 2 variable is a function of your data (reality), assumed error bars (uncertainty), and the PDF (theory) The definition is. X = 2 n h(xi) Np(xi)
2.4 CATEGORY 4 CATEGORY 5 CATEGORY 6 x 1 1 s 1 1 3 SS between within 0 MS G) Single Sample t-Statistic (Ch. 7) t= Q−μ sM s Q= s √n OR s Q=√ s2 n H) Independent Measures & Two Samples t-Statistic (Ch. 8) t= :M1−M2 ;− :μ1−μ2 ; s Q− Q 2 x If sample sizes are the same: s Q 1− Q2=√ s1 2 n +s2 n2 If the sample sizes are different ...
TI-84 Calculator Instructions for Mean, Variance & Standard Deviation. Select [STAT] then (1:Edit). Make sure the cursor is in the list, not on the list name and type the desired values pressing [ENTER] after each one. For x and P(x) data pairs, enter all x-values in one list.
052 0.035 0.022 0.013 0.007 0.0047 Random NumbersThe below table presents a typical series of ran. om numbers for the convenience of class exercises. For practical work, reference should be made to a more extensive series such. 99050. 30876. 80821. 14955.
