Read data:
x = c(1.3, 7, 3.6, 4.1, 5)
Calculate mean:
mean(x)
## [1] 4.2
Store mean of x in mx:
mx = mean(x)
Calculate deviations from mean (2 possible ways):
devx1 = x - mean(x) # Using the mean directly
devx2 = x - mx # Using the mean stored in mx
# Lets look at them, side-by-side
cbind(devx1, devx2)
## devx1 devx2
## [1,] -2.9 -2.9
## [2,] 2.8 2.8
## [3,] -0.6 -0.6
## [4,] -0.1 -0.1
## [5,] 0.8 0.8
The sum should be zero
sum(devx1)
## [1] -1.332e-15
sum(devx2)
## [1] -1.332e-15
In practice, -1.3323 × 10-15 is equal to zero, due to rounding it is a pretty small number. We can use round() to round off:
round(sum(devx1), 3)
## [1] 0
rm(list = ls()) # remove and clean up ALL objects
Read data:
x = c(41, 15, 39, 54, 31, 15, 33)
Find mean, median and mode:
mean(x)
## [1] 32.57
median(x)
## [1] 33
To get the mode we need the package “modeest”
library(modeest)
## This is package 'modeest' written by P. PONCET. For a complete list of
## functions, use 'library(help = "modeest")' or 'help.start()'.
mlv(x, method = "mfv")
## Mode (most likely value): 15
## Bickel's modal skewness: 0.7143
## Call: mlv.default(x = x, method = "mfv")
rm(list = ls()) # remove and clean up ALL objects
Read data:
x = c(2, 8, 6, 4, 10, 6, 8, 4)
We use a version of the GM formula derived from: http://en.wikipedia.org/wiki/Geometric_mean
exp(mean(log(x)))
## [1] 5.413
Read data:
Orange = c(20, 40, 50, 60, 80)
mean(Orange)
## [1] 50
median(Orange)
## [1] 50
range(Orange)
## [1] 20 80
deviation = Orange - mean(Orange)
deviation
## [1] -30 -10 0 10 30
absolute.deviation = abs(deviation)
absolute.deviation
## [1] 30 10 0 10 30
MD = sum(absolute.deviation)/length(Orange)
MD
## [1] 16
rm(list = ls()) # remove and clean up ALL objects
Read data:
x = c(12, 20, 16, 18, 19)
cbind(mean(x), x - mean(x), (x - mean(x))^2) # Table from example solution
## [,1] [,2] [,3]
## [1,] 17 -5 25
## [2,] 17 3 9
## [3,] 17 -1 1
## [4,] 17 1 1
## [5,] 17 2 4
s2 = sum((x - mean(x))^2)/(length(x) - 1)
s2
## [1] 10
s = sqrt(s2)
s
## [1] 3.162
# Use built in R functions
var(x)
## [1] 10
sd(x)
## [1] 3.162