# Frequency Distributions & Graphs Frequency Distributions & Graphs Wed, Feb 11th, 2004 Frequency Distributions Organize data into a table showing # observations in each category Includes category, its frequency (f), and its proportion (P) Proportion (P) = f / N (total sample size) Score f P 10

32 .31 9 45 .43 8 27 .26 Total 104 (cont.) If too many categories, use grouped freq distribution (you decide the appropriate class interval) Exam Score 90-100 80-89

70-79 Total f 12 15 8 35 % 34.3% 42.9% 22.8%

100% (cont.) May prefer Cumulative Distributions to show cumulative freq or prop/%: Show f or p at or below each category (label cf or cp) Add f or p for each category to total f or p for all previous categories Score f P cf cP

10 32 .31 104 1.00 9 45 .43 72 .69 8 27 .26 27 .26 Total 104 Graphs Bar chart shows frequency of nominal/ ordinal variables. Indicates frequency or % on y axis,

categories on x axis; bars do not touch Example: Histogram shows frequency of interval/ratio variables Frequency or % on y axis, order values from low to high on x axis; bars touch Example: (cont.) Frequency polygon same as histogram, but instead of bars, use points at midpoint, connect w/lines

Time Series Chart is similar w/time on x axis Examples: Shapes of Distributions Examine histogram, bar graph, look at overall shape: Bell-shaped distribution most scores in middle; fewer at extremes Positively skewed distribution: most scores at low end of scale, tail of distribution points to high (pos) end Negatively skewed distribution: most

scores at high end of scale, tail points to low (neg) end of scale A note on HW4 HW4 due Monday Ch 2 # 1, 6, 10, 13 and SPSS problems 1a-1d (all parts of #1) and 3a & 3b at end of ch 2 Youll need the data GSS98PFP-A to do the SPSS hw problems If you have the book CD-rom, its on there if not, let me know now and Ill email you the data file.

SPSS -Graphs Use student.sav data in link in lab Use menus at top: For tables, use Analyze Descriptive Statistics Frequencies Then indicate variables you want in table, hit OK Switches to output window Switch back to data view to do more analyses SPSS (cont.)

For graphs, use menu Graph, then bar graph or histogram Examine shapes of these distributions NOTE: skip Stem & Leaf Plot section of the lab and #12