Unformatted text preview: Describing Data Describing
Measures of Central Tendency Measures of Central Tendency Measures
Descriptive statistics providing a brief summary Descriptive of the center point of a distribution of Mean The sum of a set of scores divided by the number of The scores scores The score value in a distribution with an equal number The of scores above and below it of The most frequently occurring score in a distribution Median Mode Mode Mode
Not as sensitive as the mean to changes Not in all scores of distribution in However, it’s dependent on just a few However, scores and is not a stable measure of central tendency central It is possible to have more than one mode, It or no mode at all… or Can be used with nominal data Can (categorical data) and with ordinal data (categorical Modes: Examples Modes:
Unimodal Scores: 4, 4, 5, 7, 10 Mode = 4 Scores: 1, 6, 8, 14, 20 Mode = ? Scores: 1, 1, 6, 6, 8, 8 Mode = ? Scores: 2, 3, 3, 3, 5, 7, 7, 7, 10 Mode = 3 & 7 Mode No Mode No mode BiModal Median Median
Less sensitive than mean to changes in Less value of scores or to extreme values value Best measure of central tendency if you Best have a skewed distribution have Can be used with ordinal data Median: Example Median:
Scores: 4, 4, 5, 7, 10 Median = 5 If there are an even number of terms take the If average of the 2 middle most scores average Median = (5+7)/2 = 6 First, be sure to reorder the data!!!!!! First, be Median = ? Reordered: 4, 5, 6, 8, 9 Reordered: Scores: 4, 4, 5, 7, 10, 12 Scores: 9, 6, 4, 5, 8 Mean Mean
This is the most sensitive measure of central This tendency tendency A change in one score changes the value of the change mean! mean! Balance point of the distribution Sum of the difference between each score and the Sum mean = 0 mean ∑(X – X) = 0 Also, sum of squared deviations from the mean Also, is a minimum is ∑(X – X)2 = a minimum Deviation scores = X – X Mean Mean
X=∑X N ∑ = sum up scores sum N = number of scores Scores  Xs: 4, 4, 5, 7, 10 X XX 4 46 = 2 4 46 = 2 46 5 56 = 1 56 7 76 = 1 10 106 = 4 ∑X = 30 ∑(X – X) =0 X = variable name for scores X = ∑X/N ∑X/N X = 30/5 X=6 N=5 X 4 4 5 7 10 (X – X) 2 2 1 1 4 (X – X)2 4 4 1 1 16 ∑X = 30, ∑(X – X) =0, ∑(X – X)2 =26, N = 5 X = 30/5 X=6 50 60 70 80 90 100 Mean = 75 Mode = 75 Median = 75 Positively Skewed (tailed) Positively
Mode = 60 Median ≈ 65 Mean ≈ 70 50 60 70 Negatively Skewed (tailed) Negatively
Mode = 95 Median ≈ 90 (Half above, half below value) Mean ≈ 85 (Balance point of distribution) 85 90 95 Example: Example: Negatively Skewed Distribution
98 96 94 94 94 92 90 83 80 40 Mean Median Mode
861/10 (94+92)/ 2 86.1 93 94 Bimodal Distribution Bimodal
Mode = 55 & 95 Median = 75 Mean = 75 55 75 95 ...
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 '07
 Walsh
 Standard Deviation, Mean, Bimodal Distribution Bimodal

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