# ABS - what is statistically special about these numbers?
set_one <- c(5, 2, 7, 3, 5, 1)
set_two <- c(9, 6, 3, 5, 8, 6)
summary(set_one)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 1.000 2.250 4.000 3.833 5.000 7.000
summary(set_two)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 3.000 5.250 6.000 6.167 7.500 9.000
# nothing seems the same here so far
# variance?
var(set_one)
#> [1] 4.966667
var(set_two)
#> [1] 4.566667
# close, but no
# standard deviation?
sd(set_one)
#> [1] 2.228602
sd(set_two)
#> [1] 2.136976
# they have the same median absolute deviation?
mad(set_one)
#> [1] 2.2239
mad(set_two)
#> [1] 2.2239
mad(set_one) == mad(set_two)
#> [1] TRUE
identical(mad(set_one), mad(set_two))
#> [1] TRUE
# Answer: they have the same median absolute deviation
# other ideas
# population vs sample standard deviation
# it won't be the same, but for the sake of being exhaustive:
# SD and var in R use n-1 for their calulation - the sample calulation
# we can try using the *population* calculation, which is dividing by n
# sum_squares = sum((xi - xbar)^2)
# var = sum_squares / n
# sd = sqrt(var)
sum_squares <- function(x){
mean_x <- mean(x)
res <- (x - mean_x)
sum(res^2)
}
sample_var <- function(x){
sum_squares(x) / (length(x))
}
sample_var(set_one)
#> [1] 4.138889
sample_var(set_two)
#> [1] 3.805556
sort(set_one)
#> [1] 1 2 3 5 5 7
sort(set_two)
#> [1] 3 5 6 6 8 9
# someone said that when ordered, they have the same mean, median, and mode
# unfortunately this isn't the case (also ordering them and taking these
# calculations doesn't change their result)
identical(summary(sort(set_one)), summary(set_one))
#> [1] TRUE
identical(summary(sort(set_two)), summary(set_two))
#> [1] TRUE
# but let's calculate the mode anyway:
modes <- function(x) {
ux <- unique(x)
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
modes(set_one)
#> [1] 5
modes(set_two)
#> [1] 6
# and show the sorting is the same
modes(sort(set_one))
#> [1] 5
modes(sort(set_two))
#> [1] 6
# graphic relationship?
plot(set_one, set_two)
# nahCreated on 2023-01-23 with reprex v2.0.2
Session info
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