::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Mean Plot for the (time) series. First the series is segmented into a number of blocks (preferably years). Then the mean, median, and midrange are computed for the set of all i-th observations of each block (eg, all values of the same month). The resulting central tendency statistics for each periodic subseries is plotted. In addition the following notched box plots are generated: the periodic subseries, the sequential blocks, and the overall statistics.

Click here to edit the underlying code of this R Module.

Enter (or paste) your data delimited by hard returns.

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Data:
112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432
Sample Range: (leave blank to include all observations)
From:
To:
# blockwidth
Chart options
Width:
Height:

Click here to edit the underlying code of this R Module.

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Cite this software as:

Wessa P., (2008), Mean Plot (v1.0.3) in Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_meanplot.wasp/

The R code is based on :

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03.

Source code of R module
1	par1 <- as.numeric(par1)
2	(n <- length(x))
3	(np <- floor(n / par1))
4	arr <- array(NA,dim=c(par1,np+1))
5	darr <- array(NA,dim=c(par1,np+1))
6	ari <- array(0,dim=par1)
7	dx <- diff(x)
8	j <- 0
9	for (i in 1:n)
10	{
11	j = j + 1
12	ari[j] = ari[j] + 1
13	arr[j,ari[j]] <- x[i]
14	darr[j,ari[j]] <- dx[i]
15	if (j == par1) j = 0
16	}
17	ari
18	arr
19	darr
20	arr.mean <- array(NA,dim=par1)
21	arr.median <- array(NA,dim=par1)
22	arr.midrange <- array(NA,dim=par1)
23	for (j in 1:par1)
24	{
25	arr.mean[j] <- mean(arr[j,],na.rm=TRUE)
26	arr.median[j] <- median(arr[j,],na.rm=TRUE)
27	arr.midrange[j] <- (quantile(arr[j,],0.75,na.rm=TRUE) + quantile(arr[j,],0.25,na.rm=TRUE)) / 2
28	}
29	overall.mean <- mean(x)
30	overall.median <- median(x)
31	overall.midrange <- (quantile(x,0.75) + quantile(x,0.25)) / 2
32	bitmap(file="plot1.png")
33	plot(arr.mean,type="b",ylab="mean",main="Mean Plot",xlab="Periodic Index")
34	mtext(paste("#blocks = ",np))
35	abline(overall.mean,0)
36	dev.off()
37	bitmap(file="plot2.png")
38	plot(arr.median,type="b",ylab="median",main="Median Plot",xlab="Periodic Index")
39	mtext(paste("#blocks = ",np))
40	abline(overall.median,0)
41	dev.off()
42	bitmap(file="plot3.png")
43	plot(arr.midrange,type="b",ylab="midrange",main="Midrange Plot",xlab="Periodic Index")
44	mtext(paste("#blocks = ",np))
45	abline(overall.midrange,0)
46	dev.off()
47	bitmap(file="plot4.png")
48	z <- data.frame(t(arr))
49	names(z) <- c(1:par1)
50	(boxplot(z,notch=TRUE,col="grey",xlab="Periodic Index",ylab="Value",main="Notched Box Plots - Periodic Subseries"))
51	dev.off()
52	bitmap(file="plot4b.png")
53	z <- data.frame(t(darr))
54	names(z) <- c(1:par1)
55	(boxplot(z,notch=TRUE,col="grey",xlab="Periodic Index",ylab="Value",main="Notched Box Plots - Differenced Periodic Subseries"))
56	dev.off()
57	bitmap(file="plot5.png")
58	z <- data.frame(arr)
59	names(z) <- c(1:np)
60	(boxplot(z,notch=TRUE,col="grey",xlab="Block Index",ylab="Value",main="Notched Box Plots - Sequential Blocks"))
61	dev.off()
62	bitmap(file="plot6.png")
63	z <- data.frame(cbind(arr.mean,arr.median,arr.midrange))
64	names(z) <- list("mean","median","midrange")
65	(boxplot(z,notch=TRUE,col="grey",ylab="Overall Central Tendency",main="Notched Box Plots"))
66	dev.off()

To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/

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Software Version : 1.1.22-r6
Algorithms & Software : Prof. dr. P. Wessa
Facilities : Resa R&D - Office for Research, Development, and Education
Server : www.wessa.net

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