data = read.csv('C:/Users/dell/Desktop/karpur.csv')
kcore= data$k.core 
depth=data$depth
summary(data)
##      depth         caliper         ind.deep          ind.med       
##  Min.   :5667   Min.   :8.487   Min.   :  6.532   Min.   :  9.386  
##  1st Qu.:5769   1st Qu.:8.556   1st Qu.: 28.799   1st Qu.: 27.892  
##  Median :5872   Median :8.588   Median :217.849   Median :254.383  
##  Mean   :5873   Mean   :8.622   Mean   :275.357   Mean   :273.357  
##  3rd Qu.:5977   3rd Qu.:8.686   3rd Qu.:566.793   3rd Qu.:544.232  
##  Max.   :6083   Max.   :8.886   Max.   :769.484   Max.   :746.028  
##      gamma            phi.N            R.deep            R.med        
##  Min.   : 16.74   Min.   :0.0150   Min.   :  1.300   Min.   :  1.340  
##  1st Qu.: 40.89   1st Qu.:0.2030   1st Qu.:  1.764   1st Qu.:  1.837  
##  Median : 51.37   Median :0.2450   Median :  4.590   Median :  3.931  
##  Mean   : 53.42   Mean   :0.2213   Mean   : 24.501   Mean   : 21.196  
##  3rd Qu.: 62.37   3rd Qu.:0.2640   3rd Qu.: 34.724   3rd Qu.: 35.853  
##  Max.   :112.40   Max.   :0.4100   Max.   :153.085   Max.   :106.542  
##        SP          density.corr          density         phi.core    
##  Min.   :-73.95   Min.   :-0.067000   Min.   :1.758   Min.   :15.70  
##  1st Qu.:-42.01   1st Qu.:-0.016000   1st Qu.:2.023   1st Qu.:23.90  
##  Median :-32.25   Median :-0.007000   Median :2.099   Median :27.60  
##  Mean   :-30.98   Mean   :-0.008883   Mean   :2.102   Mean   :26.93  
##  3rd Qu.:-19.48   3rd Qu.: 0.002000   3rd Qu.:2.181   3rd Qu.:30.70  
##  Max.   : 25.13   Max.   : 0.089000   Max.   :2.387   Max.   :36.30  
##      k.core            Facies          phi.core.frac   
##  Min.   :    0.42   Length:819         Min.   :0.1570  
##  1st Qu.:  657.33   Class :character   1st Qu.:0.2390  
##  Median : 1591.22   Mode  :character   Median :0.2760  
##  Mean   : 2251.91                      Mean   :0.2693  
##  3rd Qu.: 3046.82                      3rd Qu.:0.3070  
##  Max.   :15600.00                      Max.   :0.3630
sorted_k = sort(kcore,decreasing = TRUE)
head(sorted_k)
## [1] 15600.00 14225.31 13544.98 13033.53 11841.74 11117.40
n = length(sorted_k)


k_percent = c(1:n)/(n+1)
summary(k_percent)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00122 0.25061 0.50000 0.50000 0.74939 0.99878


mod1=lm(log10(sorted_k) ~ k_percent)
plot(k_percent, sorted_k, log="y", lwd = 2)
abline(mod1)

k50=10^predict(mod1,data.frame(k_percent=c(0.5)))
k84.1=10^predict(mod1,data.frame(k_percent=c(0.841)))

V=(k50 - k84.1)/(k50)
print(V)
##         1 
## 0.7661618