::Free Statistics and Forecasting Software::

v1.2.1

:: Univariate Summary Statistics - Free Statistics Software (Calculator) ::

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 descriptive, summarizing statistics for any univariate data series. This computation includes the following statistics: central tendency, variability, quantiles, histogram, and kernel density.

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

 Send output to: Browser Blue - Charts White Browser Black/White CSV Data[reset 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 Chart options Width: Height: Y-axis minimum Y-axis maximum

 Source code of R module library(car) load(file="createtable") hyperlink <- function(url,anchor,title,target=\"_blank\"){ anchor } x <-sort(x[!is.na(x)]) num <- 50 res <- array(NA,dim=c(num,3)) geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } iqd <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } iqdiff <- qvalue3 - qvalue1 return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1))) } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } range <- max(x) - min(x) lx <- length(x) biasf <- (lx-1)/lx varx <- var(x) bvarx <- varx*biasf sdx <- sqrt(varx) mx <- mean(x) bsdx <- sqrt(bvarx) x2 <- x*x mse0 <- sum(x2)/lx xmm <- x-mx xmm2 <- xmm*xmm msem <- sum(xmm2)/lx axmm <- abs(x - mx) medx <- median(x) axmmed <- abs(x - medx) xmmed <- x - medx xmmed2 <- xmmed*xmmed msemed <- sum(xmmed2)/lx qarr <- array(NA,dim=c(8,3)) for (j in 1:8) { qarr[j,] <- iqd(x,j) } sdpo <- 0 adpo <- 0 for (i in 1:(lx-1)) { for (j in (i+1):lx) { ldi <- x[i]-x[j] aldi <- abs(ldi) sdpo = sdpo + ldi * ldi adpo = adpo + aldi } } denom <- (lx*(lx-1)/2) sdpo = sdpo / denom adpo = adpo / denom gmd <- 0 for (i in 1:lx) { for (j in 1:lx) { ldi <- abs(x[i]-x[j]) gmd = gmd + ldi } } gmd <- gmd / (lx*(lx-1)) sumx <- sum(x) pk <- x / sumx ck <- cumsum(pk) dk <- array(NA,dim=lx) for (i in 1:lx) { if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i] } bigd <- sum(dk) * 2 / (lx-1) iod <- 1 - sum(pk*pk) res[1,] <- c("Absolute range","http://www.xycoon.com/absolute.htm", signif(range,6)) res[2,] <- c("Relative range (unbiased)","http://www.xycoon.com/relative.htm", signif(range/sd(x),6)) res[3,] <- c("Relative range (biased)","http://www.xycoon.com/relative.htm", signif(range/sqrt(varx*biasf),6)) res[4,] <- c("Variance (unbiased)","http://www.xycoon.com/unbiased.htm", signif(varx,6)) res[5,] <- c("Variance (biased)","http://www.xycoon.com/biased.htm", signif(bvarx,6)) res[6,] <- c("Standard Deviation (unbiased)","http://www.xycoon.com/unbiased1.htm", signif(sdx,6)) res[7,] <- c("Standard Deviation (biased)","http://www.xycoon.com/biased1.htm", signif(bsdx,6)) res[8,] <- c("Coefficient of Variation (unbiased)","http://www.xycoon.com/variation.htm", signif(sdx/mx,6)) res[9,] <- c("Coefficient of Variation (biased)","http://www.xycoon.com/variation.htm", signif(bsdx/mx,6)) res[10,] <- c("Mean Squared Error (MSE versus 0)","http://www.xycoon.com/mse.htm", signif(mse0,6)) res[11,] <- c("Mean Squared Error (MSE versus Mean)","http://www.xycoon.com/mse.htm", signif(msem,6)) res[12,] <- c("Mean Absolute Deviation from Mean (MAD Mean)", "http://www.xycoon.com/mean2.htm", signif(sum(axmm)/lx,6)) res[13,] <- c("Mean Absolute Deviation from Median (MAD Median)", "http://www.xycoon.com/median1.htm", signif(sum(axmmed)/lx,6)) res[14,] <- c("Median Absolute Deviation from Mean", "http://www.xycoon.com/mean3.htm", signif(median(axmm),6)) res[15,] <- c("Median Absolute Deviation from Median", "http://www.xycoon.com/median2.htm", signif(median(axmmed),6)) res[16,] <- c("Mean Squared Deviation from Mean", "http://www.xycoon.com/mean1.htm", signif(msem,6)) res[17,] <- c("Mean Squared Deviation from Median", "http://www.xycoon.com/median.htm", signif(msemed,6)) mylink1 <- hyperlink("http://www.xycoon.com/difference.htm","Interquartile Difference","") mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ") res[18,] <- c("", mylink2, signif(qarr[1,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ") res[19,] <- c("", mylink2, signif(qarr[2,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ") res[20,] <- c("", mylink2, signif(qarr[3,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ") res[21,] <- c("", mylink2, signif(qarr[4,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ") res[22,] <- c("", mylink2, signif(qarr[5,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ") res[23,] <- c("", mylink2, signif(qarr[6,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ") res[24,] <- c("", mylink2, signif(qarr[7,1],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ") res[25,] <- c("", mylink2, signif(qarr[8,1],6)) mylink1 <- hyperlink("http://www.xycoon.com/deviation.htm","Semi Interquartile Difference","") mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ") res[26,] <- c("", mylink2, signif(qarr[1,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ") res[27,] <- c("", mylink2, signif(qarr[2,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ") res[28,] <- c("", mylink2, signif(qarr[3,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ") res[29,] <- c("", mylink2, signif(qarr[4,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ") res[30,] <- c("", mylink2, signif(qarr[5,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ") res[31,] <- c("", mylink2, signif(qarr[6,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ") res[32,] <- c("", mylink2, signif(qarr[7,2],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ") res[33,] <- c("", mylink2, signif(qarr[8,2],6)) mylink1 <- hyperlink("http://www.xycoon.com/variation1.htm","Coefficient of Quartile Variation","") mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ") res[34,] <- c("", mylink2, signif(qarr[1,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ") res[35,] <- c("", mylink2, signif(qarr[2,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ") res[36,] <- c("", mylink2, signif(qarr[3,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ") res[37,] <- c("", mylink2, signif(qarr[4,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ") res[38,] <- c("", mylink2, signif(qarr[5,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ") res[39,] <- c("", mylink2, signif(qarr[6,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ") res[40,] <- c("", mylink2, signif(qarr[7,3],6)) mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ") res[41,] <- c("", mylink2, signif(qarr[8,3],6)) res[42,] <- c("Number of all Pairs of Observations", "http://www.xycoon.com/pair_numbers.htm", signif(lx*(lx-1)/2,6)) res[43,] <- c("Squared Differences between all Pairs of Observations", "http://www.xycoon.com/squared_differences.htm", signif(sdpo,6)) res[44,] <- c("Mean Absolute Differences between all Pairs of Observations", "http://www.xycoon.com/mean_abs_differences.htm", signif(adpo,6)) res[45,] <- c("Gini Mean Difference", "http://www.xycoon.com/gini_mean_difference.htm", signif(gmd,6)) res[46,] <- c("Leik Measure of Dispersion", "http://www.xycoon.com/leiks_d.htm", signif(bigd,6)) res[47,] <- c("Index of Diversity", "http://www.xycoon.com/diversity.htm", signif(iod,6)) res[48,] <- c("Index of Qualitative Variation", "http://www.xycoon.com/qualitative_variation.htm", signif(iod*lx/(lx-1),6)) res[49,] <- c("Coefficient of Dispersion", "http://www.xycoon.com/dispersion.htm", signif(sum(axmm)/lx/medx,6)) res[50,] <- c("Observations", "", lx) print(res) (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) print(midm) bitmap(file="test1.png") lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == "") | (ylimmax == "")) plot(win[,1],type="b",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Winsorized Mean(j/n)", ylim=c(min(lb),max(ub))) else plot(win[,1],type="l",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Winsorized Mean(j/n)", ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file="test2.png") lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == "") | (ylimmax == "")) plot(tri[,1],type="b",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Trimmed Mean(j/n)", ylim=c(min(lb),max(ub))) else plot(tri[,1],type="l",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Trimmed Mean(j/n)", ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() a<-table.start() a<-table.row.start(a) a<-table.element(a,"Central Tendency - Ungrouped Data",4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Measure",header=TRUE) a<-table.element(a,"Value",header=TRUE) a<-table.element(a,"S.E.",header=TRUE) a<-table.element(a,"Value/S.E.",header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/arithmetic_mean.htm", "Arithmetic Mean", "click to view the definition of the Arithmetic Mean"),header=TRUE) a<-table.element(a,signif(arm,6)) a<-table.element(a,hyperlink("http://www.xycoon.com/arithmetic_mean_standard_error.htm", signif(armse,6), "click to view the definition of the Standard Error of the Arithmetic Mean")) a<-table.element(a,signif(armose,6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/geometric_mean.htm", "Geometric Mean", "click to view the definition of the Geometric Mean"),header=TRUE) a<-table.element(a,signif(geo,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/harmonic_mean.htm", "Harmonic Mean", "click to view the definition of the Harmonic Mean"),header=TRUE) a<-table.element(a,signif(har,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/quadratic_mean.htm", "Quadratic Mean", "click to view the definition of the Quadratic Mean"),header=TRUE) a<-table.element(a,signif(qua,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste("Winsorized Mean (",j) mylabel <- paste(mylabel,"/") mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,")") a<-table.element(a,hyperlink("http://www.xycoon.com/winsorized_mean.htm", mylabel, "click to view the definition of the Winsorized Mean"),header=TRUE) a<-table.element(a,signif(win[j,1],6)) a<-table.element(a,signif(win[j,2],6)) a<-table.element(a,signif(win[j,1]/win[j,2],6)) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste("Trimmed Mean (",j) mylabel <- paste(mylabel,"/") mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,")") a<-table.element(a,hyperlink("http://www.xycoon.com/arithmetic_mean.htm", mylabel, "click to view the definition of the Trimmed Mean"),header=TRUE) a<-table.element(a,signif(tri[j,1],6)) a<-table.element(a,signif(tri[j,2],6)) a<-table.element(a,signif(tri[j,1]/tri[j,2],6)) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/median_1.htm", "Median", "click to view the definition of the Median"),header=TRUE) a<-table.element(a,signif(median(x),6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/midrange.htm", "Midrange", "click to view the definition of the Midrange"),header=TRUE) a<-table.element(a,signif(midr,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_1.htm","Weighted Average at Xnp",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[1],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_2.htm","Weighted Average at X(n+1)p",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[2],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_3.htm","Empirical Distribution Function",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[3],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_4.htm","Empirical Distribution Function - Averaging",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[4],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_5.htm","Empirical Distribution Function - Interpolation",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[5],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_6.htm","Closest Observation",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[6],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_7.htm","True Basic - Statistics Graphics Toolkit",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[7],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean") mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_8.htm","MS Excel (old versions)",""),sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[8],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of observations",header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Variability - Ungrouped Data",2,TRUE) a<-table.row.end(a) for (i in 1:num) { a<-table.row.start(a) if (res[i,1] != "") { a<-table.element(a,hyperlink(res[i,2],res[i,1],""),header=TRUE) } else { a<-table.element(a,res[i,2],header=TRUE) } a<-table.element(a,res[i,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable1.tab") lx <- length(x) qval <- array(NA,dim=c(99,8)) mystep <- 25 mystart <- 25 if (lx>10){ mystep=10 mystart=10 } if (lx>20){ mystep=5 mystart=5 } if (lx>50){ mystep=2 mystart=2 } if (lx>=100){ mystep=1 mystart=1 } for (perc in seq(mystart,99,mystep)) { qval[perc,1] <- q1(x,lx,perc/100,i,f) qval[perc,2] <- q2(x,lx,perc/100,i,f) qval[perc,3] <- q3(x,lx,perc/100,i,f) qval[perc,4] <- q4(x,lx,perc/100,i,f) qval[perc,5] <- q5(x,lx,perc/100,i,f) qval[perc,6] <- q6(x,lx,perc/100,i,f) qval[perc,7] <- q7(x,lx,perc/100,i,f) qval[perc,8] <- q8(x,lx,perc/100,i,f) } bitmap(file="test3.png") qqPlot(x,dist="norm",main="QQ plot (Normal) with confidence intervals") grid() dev.off() a<-table.start() a<-table.row.start(a) a<-table.element(a,"Percentiles - Ungrouped Data",9,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p",1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_1.htm", "Weighted Average at Xnp",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_2.htm","Weighted Average at X(n+1)p",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_3.htm","Empirical Distribution Function",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_4.htm","Empirical Distribution Function - Averaging",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_5.htm","Empirical Distribution Function - Interpolation",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_6.htm","Closest Observation",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_7.htm","True Basic - Statistics Graphics Toolkit",""),1,TRUE) a<-table.element(a,hyperlink("http://www.xycoon.com/method_8.htm","MS Excel (old versions)",""),1,TRUE) a<-table.row.end(a) for (perc in seq(mystart,99,mystep)) { a<-table.row.start(a) a<-table.element(a,round(perc/100,2),1,TRUE) for (j in 1:8) { a<-table.element(a,round(qval[perc,j],6)) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable2.tab") bitmap(file="histogram1.png") myhist<-hist(x) dev.off() myhist n <- length(x) a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink("http://www.xycoon.com/histogram.htm","Frequency Table (Histogram)",""),6,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Bins",header=TRUE) a<-table.element(a,"Midpoint",header=TRUE) a<-table.element(a,"Abs. Frequency",header=TRUE) a<-table.element(a,"Rel. Frequency",header=TRUE) a<-table.element(a,"Cumul. Rel. Freq.",header=TRUE) a<-table.element(a,"Density",header=TRUE) a<-table.row.end(a) crf <- 0 mybracket <- "[" mynumrows <- (length(myhist\$breaks)-1) for (i in 1:mynumrows) { a<-table.row.start(a) if (i == 1) dum <- paste("[",myhist\$breaks[i],sep="") else dum <- paste(mybracket,myhist\$breaks[i],sep="") dum <- paste(dum,myhist\$breaks[i+1],sep=",") if (i==mynumrows) dum <- paste(dum,"]",sep="") else dum <- paste(dum,mybracket,sep="") a<-table.element(a,dum,header=TRUE) a<-table.element(a,myhist\$mids[i]) a<-table.element(a,myhist\$counts[i]) rf <- myhist\$counts[i]/n crf <- crf + rf a<-table.element(a,round(rf,6)) a<-table.element(a,round(crf,6)) a<-table.element(a,round(myhist\$density[i],6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable5.tab") bitmap(file="density1.png") mydensity1<-density(x,kernel="gaussian",na.rm=TRUE) plot(mydensity1,main="Gaussian Kernel") grid() dev.off() mydensity1 a<-table.start() a<-table.row.start(a) a<-table.element(a,"Properties of Density Trace",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Bandwidth",header=TRUE) a<-table.element(a,mydensity1\$bw) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"#Observations",header=TRUE) a<-table.element(a,mydensity1\$n) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable4.tab")
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 Cite this software as: Wessa P., (2017), Univariate Summary Statistics (v1.0.8) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_summary1.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/
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 To cite Wessa.net in publications use:Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education, version 1.2.1, URL https://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.2.1Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net
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