Ukuran Pemutusan Data
Menghitung Mean, Median, Modus Data Berkelompok
1 Mean Data Berkelompok (Rata-rata Data Berkelompok)
1.1 Definisi Mean Data Berkelompok
Mean (rata-rata) untuk data kelompok adalah nilai rata-rata yang dihitung berdasarkan frekuensi kelas. Untuk data kelompok, mean dihitung dengan rumus: \[ \text{Mean} = \frac{\sum f_i \cdot x_i}{\sum f_i} \]
Dimana:
\(f_i\) = frekuensi ke-\(i\)
\(x_i\) = titik tengah ke-\(i\)
\(\sum f_i \cdot x_i\) = jumlah hasil perkalian antara frekuensi dan titik tengah
\(\sum f_i\) = jumlah total frekuensi
1.2 Langkah-langkah Menghitung Mean
Tentukan titik tengah (\(x_i\))
Kalikan frekuensi (\(f_i\))
Jumlahkan hasil perkalian, yaitu \(\sum f_i \cdot x_i\).
Jumlahkan frekuensi untuk mendapatkan \(\sum f_i\)
1.3 Contoh Mean Data Berkelompok
| Nilai | Frekuensi |
|---|---|
| 80 | 5 |
| 85 | 12 |
| 90 | 8 |
| 95 | 4 |
| 100 | 5 |
Menghitung \(f_i \cdot x_i\):
\(5 \cdot 80 = 400\)
\(12 \cdot 85 = 1020\)
\(8 \cdot 90 = 720\)
\(4 \cdot 95 = 380\)
\(6 \cdot 100 = 600\)
Menjumlahkan \(f_i \cdot x_i\): \[ \sum f_i \cdot x_i = 400 + 1020 + 720 + 380 + 600 = 3120 \]
Menjumlahkan Frekuensi: \[ \sum f_i = 5 + 12 + 8 + 4 + 6 = 35 \]
Menghitung Mean: \[ \text{Mean} = \frac{3120}{35} \approx 89.14 \]
Jadi, mean data ini adalah sekitar 89.14.
1.4 Mean Data Kelompok dalam Boxplot
## Mean data berkelompok: 89.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