Histograms discovering Objectives Create and interpret frequency polygons Create and interpret accumulation frequency polygons Create and also interpret overlaid frequency polygon

Frequency polygons are a graphical an equipment for understanding the shapes of distributions. They serve the same objective as histograms, but are especially helpful for comparing sets of data. Frequency polygons are likewise a good choice because that displaying accumulation frequency distributions.

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To develop a frequency polygon, start just as because that histograms, by selecting a course interval. Then draw an X-axis representing the values of the scores in her data. Mark the middle of each course interval v a tick mark, and also label it with the center value stood for by the class. Draw the Y-axis to indicate the frequency of every class. Location a suggest in the middle of each course interval in ~ the height matching to the frequency. Finally, attach the points. Girlfriend should incorporate one class interval below the lowest worth in her data and also one above the highest value. The graph will then touch the X-axis ~ above both sides.

A frequency polygon because that 642 psychology test scores presented in figure 1 was created from the frequency table presented in Table 1.

Table 1. Frequency distribution of Psychology check Scores.

lower LimitUpper LimitCountCumulative Count 29.5 39.5 0 0 39.549.53349.559.5101359.569.5536669.579.510717379.589.514732089.599.513045099.5109.578528109.5119.559587119.5129.536623129.5139.511634139.5149.56640149.5159.51641159.5169.51642 169.5 179.5 0 642

The first label ~ above the X-axis is 35. This represents an interval extending from 29.5 come 39.5. Because the lowest check score is 46, this interval has actually a frequency that 0. The suggest labeled 45 represents the interval indigenous 39.5 to 49.5. There are three scores in this interval. There space 147 scores in the interval that surrounds 85.

You can easily discern the form of the distribution from number 1. Most of the scores are between 65 and 115. The is clear that the circulation is no symmetric inasmuch as great scores (to the right) trace off more gradually than poor scores (to the left). In the terminology of chapter 3 (where we will certainly study shapes of distributions an ext systematically), the distribution is skewed.


number 1. Frequency polygon for the psychology test scores.

A cumulative frequency polygon for the very same test scores is shown in figure 2. The graph is the exact same as before except that the Y value for each point is the variety of students in the corresponding course interval plus all numbers in lower intervals. For example, there room no scores in the interval labeling "35," three in the interval "45," and also 10 in the term "55." Therefore, the Y value corresponding to "55" is 13. Due to the fact that 642 students take it the test, the cumulative frequency for the critical interval is 642.

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number 2. Cumulative frequency polygon for the psychology test scores.

Frequency polygon are advantageous for compare distributions. This is accomplished by overlaying the frequency polygons attracted for different data sets. Figure 3 gives an example. The data come from a job in i beg your pardon the score is to relocate a computer cursor to a target on the display as quick as possible. ~ above 20 of the trials, the target was a little rectangle; ~ above the various other 20, the target was a big rectangle. Time to reach the target was tape-recorded on every trial. The two distributions (one for each target) are plotted together in figure 3. The number shows that, although over there is part overlap in times, it usually took much longer to move the cursor to the tiny target than to the big one.


number 3. Overlaid frequency polygons.

It is also possible to plot 2 cumulative frequency distribution in the same graph. This is shown in number 4 utilizing the same data from the cursor task. The difference in distributions because that the two targets is again evident.


figure 4. Overlaid cumulative frequency polygons.

keep in mind that the graphs ~ above this web page were not created in R. However, the R code displayed here to produce very comparable graphs. Make sure to put the data papers in the default directory. R code written by David Scott

Data documents for numbers 1 and 2 Data files for figures 3 and 4 # figure 1 test = read.csv(file = "psych_scores.csv") bk = seq(40,170,10) # bin counting interval tk = seq(35,175,10) # FP "bins" edges nuk = c( 0, hist( (tests<<1>>), bk, plot=F )$counts, 0 ) main="Frequency polygon because that the psychology test scores" plot(tk,nuk,type="l",col=4,xlab="Test Score",ylab="Frequency",lwd=2,main=main,ylim=c(0,160)) points(tk,nuk,pch=16,col=4,cex=1.5); abline(h=seq(0,160,20),lwd=.5) # number 2 tests = read.csv(file = "psych_scores.csv") cum.nuk = cumsum(nuk) main="Cumulative frequency polygon because that the psychology test scores" plot(tk,cum.nuk,type="l",col=4,xlab="Test Score",ylab="Cumulative Frequency", lwd=2,main=main,ylim=c(0,700)) points(tk,cum.nuk,pch=16,col=4,cex=1.5); abline(h=seq(0,700,100),lwd=.5) # number 3 target = read.csv(file = "target_size.csv") bk = seq(400,1100,100) # bin count interval tk = seq(350,1150,100) # FP "bins" edges dat = target<<2>> # 1st 20 small 2nd 20 big nuk1 = c( 0, hist( dat< 1:20>, bk, plot=F )$counts, 0 ) nuk2 = c( 0, hist( dat<21:40>, bk, plot=F )$counts, 0 ) main="Overlaid Frequency polygons" plot(tk,nuk1,type="l",col=2,xlab="Time (msec)",ylab="Frequency",lwd=2,main=main,ylim=c(0,10)) points(tk,nuk1,pch=16,col=2,cex=2); abline(h=seq(0,10,2.5),lwd=.5,lty=2) lines(tk,nuk2,col=4); points(tk,nuk2,pch=16,cex=2,col=4) text(1000,4,"small target",cex=1.5) text(720,8,"large target",cex=1.5) # number 4 target = read.csv(file = "target_size.csv") cum.nuk1 = cumsum(nuk1) cum.nuk2 = cumsum(nuk2) main="Overlaid accumulation frequency polygons" plot(tk,cum.nuk1,type="l",col=2,xlab="Time (msec)", ylab="Cumulative Frequency", lwd=2,main=main,ylim=c(0,20)) points(tk,cum.nuk1,pch=16,col=2,cex=2); abline(h=seq(0,20,5)) lines(tk,cum.nuk2,col=4,lwd=2); points(tk,cum.nuk2,pch=16,col=4,cex=2) text(850,12,"small target",cex=1.5) text(450,18,"large target",cex=1.5)