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Frequency Distributions
PSY 211
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Frequency Distribution
Definition: Table/graph showing number of participants in each category x f Basketball 23 Baseball 17 Football 29 Other 7
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If I gave a 5-point quiz to a class, the distribution of scores might look like this:
X f 5 12 4 19 3 11 2 6 1 9
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Find the proportion (p) of people who have each score. p = f / N
X f p 5 12 .20 4 19 .32 3 11 .18 2 6 .10 1 9 .15 .05
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Find the percentage (%) of people who have each score. % = p * 100
X f p % 5 12 .20 20 4 19 .32 32 3 11 .18 18 2 6 .10 10 1 9 .15 15 .05
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If the scores are spread out, it is okay to group them into a range of scores
Some data: 96, 68, 74, 82, 86, 51, 66, 82, 91, 85, 77,89,88,88,61,90, 79,86,80,92,88,69, 44,99,81,82 X f 91-100 5 81-90 12 71-80 3 61-70 4 51-60 1 41-50
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Turn a frequency table into a histogram:
X f 5 12 4 19 3 11 2 6 1 9 Scores
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Turn a frequency table into a histogram:
X f 5 12 4 19 3 11 2 6 1 9 f Scores
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Histogram of Quiz Scores
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Now turn that histogram (bar graph) into a polygon (shape, line graph)
Polygon of Quiz Scores f 6 Scores
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You could graph relative frequencies (percentages) instead of frequencies
X f p % 5 12 .20 20 4 19 .32 32 3 11 .18 18 2 6 .10 10 1 9 .15 15 .05 % Scores
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Relative Histogram of Quiz Scores
% Scores
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Distribution Shape Rather than graph an entire distribution, sometimes researchers just describe its shape and provide a few statistics f x
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f Symmetrical distributions: look the same on both sides, mirror images x f x
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Positive Skew *Skewed distribution: lopsided, have a tail off to one side Tail indicates the direction of the skew (+ or -) f x Negative Skew f x
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Negative Skew In actuality, frequency polygons look more like these f x f Symmetrical x
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Percentile Rank Used to describe where a score falls in a given distribution 50th percentile 95th percentile f f x x
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Finding Percentile Ranks
cf = cumulative frequency, number of people with that score or lower X f cf 5 12 60 4 19 48 3 11 29 2 6 18 1 9
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Finding Percentile Ranks
X f cf c% 5 12 60 100% 4 19 48 80% 3 11 29 48% 2 6 18 30% 1 9 20% 5% c% = cumulative percentage or percentile rank, percent with that score or lower
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