::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 following statistics: absolute range, relative range, variance, standard error, coefficient of variation, mean squared error, mean absolute deviation, median absolute deviation, mean squared deviation, interquartile difference, semi interquartile difference, coefficient of quartile variation, number of pairs of observations, squared differences between observations, mean absolute differences between observations, Gini mean difference, Leik measure of dispersion, index of diversity, index of qualitative variation, and coefficient of dispersion.

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

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

---

Source code of R module
1	num <- 50
2	res <- array(NA,dim=c(num,3))
3	q1 <- function(data,n,p,i,f) {
4	np <- n*p;
5	i <<- floor(np)
6	f <<- np - i
7	qvalue <- (1-f)*data[i] + f*data[i+1]
8	}
9	q2 <- function(data,n,p,i,f) {
10	np <- (n+1)*p
11	i <<- floor(np)
12	f <<- np - i
13	qvalue <- (1-f)*data[i] + f*data[i+1]
14	}
15	q3 <- function(data,n,p,i,f) {
16	np <- n*p
17	i <<- floor(np)
18	f <<- np - i
19	if (f==0) {
20	qvalue <- data[i]
21	} else {
22	qvalue <- data[i+1]
23	}
24	}
25	q4 <- function(data,n,p,i,f) {
26	np <- n*p
27	i <<- floor(np)
28	f <<- np - i
29	if (f==0) {
30	qvalue <- (data[i]+data[i+1])/2
31	} else {
32	qvalue <- data[i+1]
33	}
34	}
35	q5 <- function(data,n,p,i,f) {
36	np <- (n-1)*p
37	i <<- floor(np)
38	f <<- np - i
39	if (f==0) {
40	qvalue <- data[i+1]
41	} else {
42	qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
43	}
44	}
45	q6 <- function(data,n,p,i,f) {
46	np <- n*p+0.5
47	i <<- floor(np)
48	f <<- np - i
49	qvalue <- data[i]
50	}
51	q7 <- function(data,n,p,i,f) {
52	np <- (n+1)*p
53	i <<- floor(np)
54	f <<- np - i
55	if (f==0) {
56	qvalue <- data[i]
57	} else {
58	qvalue <- f*data[i] + (1-f)*data[i+1]
59	}
60	}
61	q8 <- function(data,n,p,i,f) {
62	np <- (n+1)*p
63	i <<- floor(np)
64	f <<- np - i
65	if (f==0) {
66	qvalue <- data[i]
67	} else {
68	if (f == 0.5) {
69	qvalue <- (data[i]+data[i+1])/2
70	} else {
71	if (f < 0.5) {
72	qvalue <- data[i]
73	} else {
74	qvalue <- data[i+1]
75	}
76	}
77	}
78	}
79	iqd <- function(x,def) {
80	x <-sort(x[!is.na(x)])
81	n<-length(x)
82	if (def==1) {
83	qvalue1 <- q1(x,n,0.25,i,f)
84	qvalue3 <- q1(x,n,0.75,i,f)
85	}
86	if (def==2) {
87	qvalue1 <- q2(x,n,0.25,i,f)
88	qvalue3 <- q2(x,n,0.75,i,f)
89	}
90	if (def==3) {
91	qvalue1 <- q3(x,n,0.25,i,f)
92	qvalue3 <- q3(x,n,0.75,i,f)
93	}
94	if (def==4) {
95	qvalue1 <- q4(x,n,0.25,i,f)
96	qvalue3 <- q4(x,n,0.75,i,f)
97	}
98	if (def==5) {
99	qvalue1 <- q5(x,n,0.25,i,f)
100	qvalue3 <- q5(x,n,0.75,i,f)
101	}
102	if (def==6) {
103	qvalue1 <- q6(x,n,0.25,i,f)
104	qvalue3 <- q6(x,n,0.75,i,f)
105	}
106	if (def==7) {
107	qvalue1 <- q7(x,n,0.25,i,f)
108	qvalue3 <- q7(x,n,0.75,i,f)
109	}
110	if (def==8) {
111	qvalue1 <- q8(x,n,0.25,i,f)
112	qvalue3 <- q8(x,n,0.75,i,f)
113	}
114	iqdiff <- qvalue3 - qvalue1
115	return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
116	}
117	range <- max(x) - min(x)
118	lx <- length(x)
119	biasf <- (lx-1)/lx
120	varx <- var(x)
121	bvarx <- varx*biasf
122	sdx <- sqrt(varx)
123	mx <- mean(x)
124	bsdx <- sqrt(bvarx)
125	x2 <- x*x
126	mse0 <- sum(x2)/lx
127	xmm <- x-mx
128	xmm2 <- xmm*xmm
129	msem <- sum(xmm2)/lx
130	axmm <- abs(x - mx)
131	medx <- median(x)
132	axmmed <- abs(x - medx)
133	xmmed <- x - medx
134	xmmed2 <- xmmed*xmmed
135	msemed <- sum(xmmed2)/lx
136	qarr <- array(NA,dim=c(8,3))
137	for (j in 1:8) {
138	qarr[j,] <- iqd(x,j)
139	}
140	sdpo <- 0
141	adpo <- 0
142	for (i in 1:(lx-1)) {
143	for (j in (i+1):lx) {
144	ldi <- x[i]-x[j]
145	aldi <- abs(ldi)
146	sdpo = sdpo + ldi * ldi
147	adpo = adpo + aldi
148	}
149	}
150	denom <- (lx*(lx-1)/2)
151	sdpo = sdpo / denom
152	adpo = adpo / denom
153	gmd <- 0
154	for (i in 1:lx) {
155	for (j in 1:lx) {
156	ldi <- abs(x[i]-x[j])
157	gmd = gmd + ldi
158	}
159	}
160	gmd <- gmd / (lx*(lx-1))
161	sumx <- sum(x)
162	pk <- x / sumx
163	ck <- cumsum(pk)
164	dk <- array(NA,dim=lx)
165	for (i in 1:lx) {
166	if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
167	}
168	bigd <- sum(dk) * 2 / (lx-1)
169	iod <- 1 - sum(pk*pk)
170	res[1,] <- c("Absolute range","http://www.xycoon.com/absolute.htm", range)
171	res[2,] <- c("Relative range (unbiased)","http://www.xycoon.com/relative.htm", range/sd(x))
172	res[3,] <- c("Relative range (biased)","http://www.xycoon.com/relative.htm", range/sqrt(varx*biasf))
173	res[4,] <- c("Variance (unbiased)","http://www.xycoon.com/unbiased.htm", varx)
174	res[5,] <- c("Variance (biased)","http://www.xycoon.com/biased.htm", bvarx)
175	res[6,] <- c("Standard Deviation (unbiased)","http://www.xycoon.com/unbiased1.htm", sdx)
176	res[7,] <- c("Standard Deviation (biased)","http://www.xycoon.com/biased1.htm", bsdx)
177	res[8,] <- c("Coefficient of Variation (unbiased)","http://www.xycoon.com/variation.htm", sdx/mx)
178	res[9,] <- c("Coefficient of Variation (biased)","http://www.xycoon.com/variation.htm", bsdx/mx)
179	res[10,] <- c("Mean Squared Error (MSE versus 0)","http://www.xycoon.com/mse.htm", mse0)
180	res[11,] <- c("Mean Squared Error (MSE versus Mean)","http://www.xycoon.com/mse.htm", msem)
181	res[12,] <- c("Mean Absolute Deviation from Mean (MAD Mean)", "http://www.xycoon.com/mean2.htm", sum(axmm)/lx)
182	res[13,] <- c("Mean Absolute Deviation from Median (MAD Median)", "http://www.xycoon.com/median1.htm", sum(axmmed)/lx)
183	res[14,] <- c("Median Absolute Deviation from Mean", "http://www.xycoon.com/mean3.htm", median(axmm))
184	res[15,] <- c("Median Absolute Deviation from Median", "http://www.xycoon.com/median2.htm", median(axmmed))
185	res[16,] <- c("Mean Squared Deviation from Mean", "http://www.xycoon.com/mean1.htm", msem)
186	res[17,] <- c("Mean Squared Deviation from Median", "http://www.xycoon.com/median.htm", msemed)
187	load(file="createtable")
188	mylink1 <- hyperlink("http://www.xycoon.com/difference.htm","Interquartile Difference","")
189	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ")
190	res[18,] <- c("", mylink2, qarr[1,1])
191	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ")
192	res[19,] <- c("", mylink2, qarr[2,1])
193	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ")
194	res[20,] <- c("", mylink2, qarr[3,1])
195	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ")
196	res[21,] <- c("", mylink2, qarr[4,1])
197	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ")
198	res[22,] <- c("", mylink2, qarr[5,1])
199	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ")
200	res[23,] <- c("", mylink2, qarr[6,1])
201	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ")
202	res[24,] <- c("", mylink2, qarr[7,1])
203	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ")
204	res[25,] <- c("", mylink2, qarr[8,1])
205	mylink1 <- hyperlink("http://www.xycoon.com/deviation.htm","Semi Interquartile Difference","")
206	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ")
207	res[26,] <- c("", mylink2, qarr[1,2])
208	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ")
209	res[27,] <- c("", mylink2, qarr[2,2])
210	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ")
211	res[28,] <- c("", mylink2, qarr[3,2])
212	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ")
213	res[29,] <- c("", mylink2, qarr[4,2])
214	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ")
215	res[30,] <- c("", mylink2, qarr[5,2])
216	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ")
217	res[31,] <- c("", mylink2, qarr[6,2])
218	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ")
219	res[32,] <- c("", mylink2, qarr[7,2])
220	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ")
221	res[33,] <- c("", mylink2, qarr[8,2])
222	mylink1 <- hyperlink("http://www.xycoon.com/variation1.htm","Coefficient of Quartile Variation","")
223	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ")
224	res[34,] <- c("", mylink2, qarr[1,3])
225	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ")
226	res[35,] <- c("", mylink2, qarr[2,3])
227	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ")
228	res[36,] <- c("", mylink2, qarr[3,3])
229	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ")
230	res[37,] <- c("", mylink2, qarr[4,3])
231	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ")
232	res[38,] <- c("", mylink2, qarr[5,3])
233	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ")
234	res[39,] <- c("", mylink2, qarr[6,3])
235	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ")
236	res[40,] <- c("", mylink2, qarr[7,3])
237	mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ")
238	res[41,] <- c("", mylink2, qarr[8,3])
239	res[42,] <- c("Number of all Pairs of Observations", "http://www.xycoon.com/pair_numbers.htm", lx*(lx-1)/2)
240	res[43,] <- c("Squared Differences between all Pairs of Observations", "http://www.xycoon.com/squared_differences.htm", sdpo)
241	res[44,] <- c("Mean Absolute Differences between all Pairs of Observations", "http://www.xycoon.com/mean_abs_differences.htm", adpo)
242	res[45,] <- c("Gini Mean Difference", "http://www.xycoon.com/gini_mean_difference.htm", gmd)
243	res[46,] <- c("Leik Measure of Dispersion", "http://www.xycoon.com/leiks_d.htm", bigd)
244	res[47,] <- c("Index of Diversity", "http://www.xycoon.com/diversity.htm", iod)
245	res[48,] <- c("Index of Qualitative Variation", "http://www.xycoon.com/qualitative_variation.htm", iod*lx/(lx-1))
246	res[49,] <- c("Coefficient of Dispersion", "http://www.xycoon.com/dispersion.htm", sum(axmm)/lx/medx)
247	res[50,] <- c("Observations", "", lx)
248	res
249	a<-table.start()
250	a<-table.row.start(a)
251	a<-table.element(a,"Variability - Ungrouped Data",2,TRUE)
252	a<-table.row.end(a)
253	for (i in 1:num) {
254	a<-table.row.start(a)
255	if (res[i,1] != "") {
256	a<-table.element(a,hyperlink(res[i,2],res[i,1],""),header=TRUE)
257	} else {
258	a<-table.element(a,res[i,2],header=TRUE)
259	}
260	a<-table.element(a,res[i,3])
261	a<-table.row.end(a)
262	}
263	a<-table.end(a)
264	table.save(a,file="mytable.tab")

Cite this software as:

Wessa P., (2008), Variability (v1.0.4) in Free Statistics Software (v1.1.23-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_variability.wasp/

The R code is based on :

Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/

To cite Wessa.net in publications use:
Wessa, P. (2010), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r6, URL http://www.wessa.net/

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Software Version : 1.1.23-r6
Algorithms & Software : Patrick Wessa, PhD
Facilities : Resa R&D - Office for Research, Development, and Education
Server : www.wessa.net

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