1. Frequency Distributions
PSY 211

2. Frequency Distribution
Definition: Table/graph showing number of participants in each category x f
Basketball 23
Baseball 17
Football 29
Other 7

3. 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

4. Find the proportion (p) of people who have each score. p = f / NX f p 5 12
.20 4 19
.32 3 11
.18 2 6
.10 1 9
.15
.05

5. Find the percentage (%) of people who have each score. % = p * 100X f p % 5 12
.20 20 4 19
.32 32 3 11
.18 18 2 6
.10 10 1 9
.15 15
.05

6. 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

7. Turn a frequency table into a histogram:X f 5 12 4 19 3 11 2 6 1 9
Scores

8. Turn a frequency table into a histogram:X f 5 12 4 19 3 11 2 6 1 9 f
Scores

9. Histogram of Quiz Scores

10. Now turn that histogram (bar graph) into a polygon (shape, line graph)
Polygon of Quiz Scores f 6
Scores

11. You could graph relative frequencies (percentages) instead of frequenciesX f p % 5 12
.20 20 4 19
.32 32 3 11
.18 18 2 6
.10 10 1 9
.15 15
.05 %
Scores

12. Relative Histogram of Quiz Scores%
Scores

13. Distribution Shape
Rather than graph an entire distribution, sometimes researchers just describe its shape and provide a few statistics f x

14. f
Symmetrical distributions: look the same on both sides, mirror images x f x

15. 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

16. Negative Skew
In actuality, frequency polygons look more like these f x f
Symmetrical x

17. Percentile Rank
Used to describe where a score falls in a given distribution
50th percentile
95th percentile f f x x

18. 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

19. Finding Percentile RanksX 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