Mack's Stats

set1 <- c(10, 2, 3, 2, 4, 2, 5)

set2 <- c(20, 12, 13, 12, 14, 12, 15)

mode <- function(x) {

ux <- unique(x)

ux[which.max(tabulate(match(x, ux)))]

}

Q1:

##set1

mean(set1)
[1] 4
median(set1)
[1] 3
mode(set1)
[1] 2

##set2

mean(set2)
[1] 14
median(set2)
[1] 13
mode(set2)
[1] 12

Q2:

##set1

range(set1)
[1] 2 10
quantile(set1)
0% 25% 50% 75% 100%
2.0 2.0 3.0 4.5 10.0
var(set1)
[1] 8.333333
sd(set1)
[1] 2.886751

##set2

range(set2)
[1] 12 20
quantile(set2)
0% 25% 50% 75% 100%
12.0 12.0 13.0 14.5 20.0
var(set2)
[1] 8.333333
sd(set2)
[1] 2.886751

Q3:

Based on these results we can see how the mean median and mode is higher in set2 than in set1 because the numbers within set2 are of higher value. In contrast, the range of set1 and set2 is the same length. The biggest thing to note is that even though the numbers in set2 are larger than set1, its variance and standard deviation are the same. This shows us that on a graph, the shape of set1’s bell curve would be the same as set2’s bell curve because even though the numbers are different, the variation of the numbers are the exact same.