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Lecture 2

Lecture 2 - Frequency Distributions, Tables vs. Graphs

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Alison Luby

PSY201H1F L2 Sept 21, 2011 ○ List of x values is way too long for simple presentation of data Frequency Distributions, Tables vs. ○  Use a Grouped Freq Distr Table Graphs  X column lists class intervals: grps of • Frequency distribution: Organized scores ○ Guidelines: tabulation of entire set of scores allowing to see big picture in data at a glance  Select intervals so have about 10 ○ Shows where each indiv is located relative class intervals to others in the distr  Class interval width should be ○ Shows whether scores are high or low, simple number (2, 5, 10, multiples of concentrated in centre or spaced apart 5 or 10)  Bottom score in each class • Places raw scores in order from highest to lowest interval should b multiple of width ○ For nominal, any order • Ex. If width is 5 then bottom score • Group together everyone w same scores  is multiple of 5: 5,10,15,20 get sense of patterns  Intervals have same width, cover • Chart, table, graph, always presents 2 complete range of scores, each score belongs in 1 interval elements: ○ Cats that make up the original • Ex. Time to complete puzzle: 23  213 range measurement scale (128,99,213,117,83,201,79,156,88,91,23,65,1 ○ Record of the frequency (# of indiv in each 41,43,52,81,126,113,166,142) cat) ○ X column (top to bottom): 200-219, 180- 199,160-179,140-159,120-139,100- Freq Distr Tables 119,80-99,60-79,40-59,20-39 • Consist of at least 2 columns: ○ X column (raw scores) measurement cats ○ Start at multiple of width, don’t leave ○ F (frequency) column out intervals even if f=0 ○ Ex. Number of cars ppl have: ○ Less groups  more info you lose, less you know about your data 1,2,1,0,3,4,0,1,1,1,2,2,3,2,3,2,1,4,0,0 • Continuous var have an infinite number X F 4 2 of possible values, so in 200-219 a could 3 3 have X = 201.9 2 5 • Measurements indicate an interval not a 1 6 single pt ○ Ex. If X = 10 then the score was btwn 9.5 0 4 & 10.5 ○ Tally freqs for each X  How often each X occurs • Grouped Freq Distr Table:Values listed in  Σf = N the intervals are called Apparent Limits  Ex. Above: Σ f = 20 of the interval • But upper & lower boundaries involve • If you are asked for ΣX, do not add up the Real Limits values in the X column so don’t use the freq ○ Ex. For X=20-39, lower & upper real limits dirt table ○ Add up all of the raw scores for X instead are 19.5 & 39.5, apparent limits are 20 & ○ ΣX = ΣfX 39 ○ Or just add fX ex. 2(4) + 3(3) … = ΣfX Freq Distr Graphs • Pic (graphical representation) of info in a freq ○ ΣX = 33 distr table ○ Use the same method to calculate ΣX 2 • Calculate proportions&percentages to • All graphs have 2 perpendicular lines called describe distr axes which typically meet at 0 ○ Proportion (aka Relative Freq) ○ X axis = Abscissa: Lists the measurement scale (the set of X values) measures fraction of total grp ○ Y axis = Ordinate: Lists the freqs associated w each score ○ General rule: Y axis height = approx 2/3  p= f/N  Σp = 1.00 - 3/4 length of X axis ○ Percentage = p(100) = f/N x (100) • When score cats consist of numerical scores from interval or ratio scale, graph  Σpercentage column = 100% should be histogram or polygon • If many X values: ○ Don’t want many rows • When the scores r measured on a nominal or • Polygons: ordinal scale, the freq distr should be ○ Centre a dot above each score so displayed in a bar graph height of dot correspond to freq • Histograms ○ Join dots w straight lines ○ List cats of measurement along X axis ○ Additional line drawn @ each end to ○ Draw a bar about each X value so: bring graph back to 0 freq  Height of bar corresponds to freq  Usually reach the x axis at a pt 1 cat for that cat below lowest score on left & 1 cat  Width of bar extends to real limits above highest score on right of the cat ○ For Grouped Distr, position each dot •  No space btwn bars directly above midpt of the Class  When data grouped into class Interval intervals, draw bar above each interval  Find midpt by avging highest & lowest so width of bar extends to real limits of score for the interval the interval ○ Similar to freq histogram ○ Ex. Freq of quiz scores – Use Reg Freq  Appropriate for plotting freq of Distr Table continuous vars  Communicates same info  Distr shape may be easier to see using polygon ○ Using Reg Freq Distr Table: ○ Ex. Freq of children’s height w class intervals – Use Grouped Freq Distr Table ○ Using Grouped Freq Distr Table - dots @ midpts ○ Could be made for puzzle scores from earlier  Usually label x axis at the midpoint of each interval • Simple & quick representation • Ex. for class scores - don’t need  Ex. For previous puzzle scores: No 0 to label each bar freq in end cats so would hit 0 in new end cats ○ To make freq chart from polygon:  Start w the dot w the highest x value ○ Usually data written in histogram forms • Nom or ord scales: ○ Score cats &X values not continuous ○ Use Bar Graph: Like histogram but spaces/gaps btwn bars  Indicate the scale is made up of distinct cats ○  Can’t assume all cats r same size ○ Ex. Number of cars ppl have – discrete not continuous, can’t have 2.5 cars so X can’t be 2.5 Shapes of Freq Distrs, Symmetrical vs. Skewed • Many pops are so large we can’t know exact # of indivs (freq) for any specific cat: Percentiles + [Percentile] Ranks + ○ So pop distr can be shown
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