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INTRODUCTION TO STATISTICAL ANALYSIS. LEARNING OBJECTIVES: After studying this chapter, a student should understand: notation used in statistics; how to represent variables in a mathematical form for statistical purposes; how to construct frequency distributions, histograms, and bar graphs;
29 Φεβ 2024 · Continuing in the context of Example 4.1.2, we find the median and quartiles. median: find \(\pi_{.5}\), such that \(F(\pi_{.5}) = 0.5 \Rightarrow \pi_{.5} = 1\) (from graph in Figure 1) 1st quartile: find \(Q_1 = \pi_{.25}\), such that \(F(\pi_{.25}) = 0.25\). For this, we use the formula and the graph of the cdf in Figure 2:
1 2 Difference of means μ-μ (independent samples) 12 12 1 2 12 22 12 /2 12 12 22 12 12 Confidence Interval when and are known ()() ( ) where Hypothesis Test when and are known ( )( ) x x E x x E Ez n n x x z n n α σσ µµ σσ σσ µµ σσ −−< − <−+ = + −− − = + 12 12 1 2 12 12 /2 12 12 12 12 Confidence Interval when and ...
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
Definition of Expectation. = E(X ) Def: Mean aka. Expected value. Let X be a random variable with p(d)f f (x). The mean, or expected value of X, denoted E(X), is defined as follows. discrete: X E(X) = xf(x) All x. assuming the sum exists. continuous: 1. E(X) = xf(x) dx. 1. assuming the integral exists.
2 Ιαν 2023 · Introduction to the formula for calculating SS for ANOVA, and to the four possible ANOVA models.
4.3 2.5 3.5 2.4 4.4 2 2 1.8 3 CATEGORY 1 CATEGORY 2 CATEGORY 3 4.3 2.5 3.5 2.4 4.4 2 2 1.8 3 CATEGORY 4 CATEGORY 5 CATEGORY 6 ∑ C) Q Definitional Formula: df : If single row of data: A) Reminder: BEDM(S)AS – Brackets, Exponents, Division, Multiplication, Sum ( ∑ ), Addition, Subtraction B) Central Tendency (Ch. 3) Population mean: µ= X R ...
