Frequency distributions & Central tendency Quantitative Methods 01:830:200:B2 Week 1, class 3 Frequency distributions Method used to see the data pattern Frequency distribution tables Frequency distribution graphs ?f = n ?X = f1(X1) + f2(X2) + f3(X3)? Percent of data in category A = f(A)/ n X-axis: Data category Y-axis: Frequency count Polyon Histograms: bars _______ _________ data Height: Frequency for the category Width: Range (real limits) of the category Bar graph: bars __________ ______________ data Relative frequency distribution Smooth curves For population distributions Shape of Distributions Symmetrical Normal bi-modal Skewed (one tail stretches out further) Positive: few people on the right (high)end of scale (income) Negative: few people on the left (low) end of scale (scores on easy exam) CENTRAL TENDANCY Central Tendancy Defining CENTER of distribution There are a number of central tendencies Mean Median Mode The mean Add up the scores and divide by n Mu (?) = ?X / N = population mean M or X-bar = ?X / n = sample mean The mean ?(X ? M) will always = _______ If we have M, n, and all but one datum, we can find the last datum Constants Adding/subtracting constants If we add the same number to every score, then the mean will __________________. Multiplying/dividing constants If we multiple every datum by the same value, then the mean will ____________________ The weighted mean How should one combine the means from two groups? M1 = 35, n1 = 7 M2 = 27, n2 = 3 Two methods (?X1 + ?X2) / n-total (245+81)/10 M1(n1/(n-total)) + M2(n2/(n-total)) 35(7/10) + 27 (3/10) The median Divides the distribution in half 50% of score fall at or below the median Often used with skewed distribution Finding the median ( 2 steps) 1 2 Median location (n + 1)/2 Mean vs. median The mean and median define the middle differently Mean based on distances Median based on number of scores The mode The most frequent score Can be used to describe nominal data Data = 2, 5, 8, 5, 7; mode = ____ Data = Fr, Am, Ch, Fr, Am, Am; mode= ______ Helpful when describing multi-modal data Symmetrical distributions Skewed distributions Which central tendency? The mean is the default; generally considered the best Median might be used when _________ _________ _________ _________ Mode used when ________ _________ Which central tendency? Defining Distributions Shape Central tendency Variability (chapter 4) We will start this next time
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