x <- c(0,340,70,140,200,180,210,150,100,130,
       140,180,190,160,290,50,220,180,200,210)

hist(x)  # plot the histogram
mean(x)  # compute the mean
abline(v = mean(x),lwd=2) #add vertical mean


#data
x <- c(0,340,70,140,200,180,210,150,100,130,
       140,180,190,160,290,50,220,180,200,210)

#find quartiles
quantile(x,prob=c(.25,.50,.75),type=2)
 
 

# The median of lower half of the observations (excluding the median itself if n is odd) is the first quartile, Q1.

sort(x)[1:10]

median(sort(x)[1:10])

# scaling properties:

x<-c(2,4,6,7,8,9)
mean(x)
sd(x)

a=3
b=2
y1=(x+a)*b
y2=(x*b)+a
mean(y1);(mean(x)+a)*b
mean(y2);(mean(x)*b)+a
sd(y1);sd(y2)
sd(x)*b


z =(x-mean(x))*1/sd(x) # expresses the number of standard deviations that x falls from the mean
z
mean(z)
sd(z)
### fin