Data

menit <- c(22, 25, 19, 30, 24, 21, 45, 23, 20, 26, 24, 22, 18, 27, 23)

Soal 1: Mean, Median, Modus

mean(menit)
## [1] 24.6
median(menit)
## [1] 23
# R tidak punya fungsi modus bawaan
modus <- function(x) {
  u <- unique(x)
  u[which.max(tabulate(match(x, u)))]
}
modus(menit)
## [1] 22

Manual: data urut: 18,19,20,21,22,22,23,23,24,24,25,26,27,30,45 (n=15). Σxᵢ = 369, x̄ = 369/15 = 24,6. Median = data ke-8 = 23. Modus = 22, 23, dan 24 (masing-masing muncul 2 kali).

Soal 2: Q1, Q3, dan IQR

# type = 6 -> posisi i(n+1)/4, sesuai rumus manual
quantile(menit, probs = c(0.25, 0.75), type = 6)
## 25% 75% 
##  21  26
IQR(menit, type = 6)
## [1] 5

Manual: Q1 pos = 1(16)/4 = 4 -> 21. Q3 pos = 3(16)/4 = 12 -> 26. IQR = 26 - 21 = 5.

Interpretasi: 50% pengguna di bagian tengah memakai EcoTrack dengan rentang 21 sampai 26 menit per hari (selisih 5 menit).

Soal 3: Varians dan Standar Deviasi

var(menit)
## [1] 41.54286
sd(menit)
## [1] 6.445375

Manual: Σ(xᵢ - x̄)² = 581,6 -> s² = 581,6/14 ≈ 41,54. s = √41,54 ≈ 6,45 menit.

Interpretasi: variasi tergolong cukup tinggi karena ada satu pengguna (45 menit) yang jauh dari mean.

Soal 4: Skewness Pearson

Sk <- 3 * (mean(menit) - median(menit)) / sd(menit)
Sk
## [1] 0.7447201
library(moments)
skewness(menit)
## [1] 2.212573

Manual: Sk = 3(24,6 - 23)/6,45 ≈ 0,74 -> positif -> menceng kanan (mean > median).