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Frequency Distributions. PSY 211 8-29-07. Frequency Distribution. Definition: Table/graph showing number of participants in each category. If I gave a 5-point quiz to a class, the distribution of scores might look like this:.

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Frequency Distributions

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Frequency Distributions

PSY 211

8-29-07


Frequency Distribution

  • Definition: Table/graph showing number of participants in each category


If I gave a 5-point quiz to a class, the distribution of scores might look like this:


Find the proportion (p) of people who have each score. p = f / N


Find the percentage (%) of people who have each score. % = p * 100


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


Turn a frequency table into a histogram:

Scores


Turn a frequency table into a histogram:

f

Scores


Histogram of Quiz Scores

f

Scores


Now turn that histogram (bar graph) into a polygon (shape, line graph)

Polygon of Quiz Scores

f

6

Scores


You could graph relative frequencies (percentages) instead of frequencies

%

Scores


Relative Histogram of Quiz Scores

%

Scores


Distribution Shape

  • Rather than graph an entire distribution, sometimes researchers just describe its shape and provide a few statistics

f

x


f

Symmetrical distributions: look the same on both sides, mirror images

x

f

x


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


Negative Skew

In actuality, frequency polygons look more like these

f

x

f

Symmetrical

x


Percentile Rank

  • Used to describe where a score falls in a given distribution

95th percentile

50th percentile

f

f

x

x


Finding Percentile Ranks

cf = cumulative frequency, number of people with that score or lower


Finding Percentile Ranks

c% = cumulative percentage or percentile rank, percent with that score or lower


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