{"id":2175,"date":"2026-04-03T20:50:48","date_gmt":"2026-04-03T20:50:48","guid":{"rendered":"https:\/\/rumahpintar.co.id\/blog\/?p=2175"},"modified":"2026-04-09T04:55:37","modified_gmt":"2026-04-09T04:55:37","slug":"apa-itu-mean-median-modus-dan-jangkauan","status":"publish","type":"post","link":"https:\/\/rumahpintar.co.id\/blog\/apa-itu-mean-median-modus-dan-jangkauan\/","title":{"rendered":"Apa Itu Mean, Median, Modus, dan Jangkauan: Kuasai Statistika untuk TKA Matematika SMP"},"content":{"rendered":"<p class=\"ds-markdown-paragraph\"><span style=\"font-size: 16px;\"><a href=\"http:\/\/rumahpintar.co.id\"><strong>Bimbel Rumah Pintar<\/strong><\/a> &#8211; <\/span>Pernahkah Anda bertanya-tanya bagaimana cara menentukan nilai rata-rata rapor? Atau bagaimana toko menentukan produk terlaris? Atau bagaimana guru mengetahui nilai tengah dari hasil ujian? Semua ini melibatkan konsep apa itu <strong>mean (rerata), median, modus, dan jangkauan (range) dari data<\/strong>.<\/p>\n<p class=\"ds-markdown-paragraph\">Kompetensi ini menguji kemampuan siswa dalam memahami konsep keempat ukuran pemusatan dan penyebaran data, mengaplikasikan rumus dan cara menentukannya, serta bernalar tingkat tinggi untuk menganalisis data, menaksir nilai yang belum diketahui, dan menyelesaikan masalah kontekstual (misalnya: rata-rata berat telur dalam kemasan).<\/p>\n<p class=\"ds-markdown-paragraph\">Artikel ini akan membahas tuntas mulai dari konsep setiap ukuran, rumus-rumus penting, cara menentukan dari data tunggal dan data berfrekuensi, strategi jitu, contoh soal TKA, hingga latihan mandiri.<\/p>\n<h2>Apa Itu Mean, Median, Modus, dan Jangkauan? Memahami Ukuran Data<\/h2>\n<p class=\"ds-markdown-paragraph\">Sebelum membahas lebih jauh, mari pahami dulu apa yang dimaksud dengan keempat ukuran statistika ini. Mean, median, dan modus adalah\u00a0<strong>ukuran pemusatan data<\/strong>\u00a0(nilai yang mewakili kumpulan data). Jangkauan adalah\u00a0<strong>ukuran penyebaran data<\/strong>\u00a0(seberapa jauh data tersebar).<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Tabel ringkasan keempat ukuran:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Ukuran<\/th>\n<th>Arti<\/th>\n<th>Fungsi<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Mean (Rata-rata)<\/td>\n<td>Jumlah semua data dibagi banyak data<\/td>\n<td>Memberikan gambaran nilai tipikal<\/td>\n<\/tr>\n<tr>\n<td>Median (Nilai Tengah)<\/td>\n<td>Nilai tengah setelah data diurutkan<\/td>\n<td>Tahan terhadap nilai ekstrem (pencilan)<\/td>\n<\/tr>\n<tr>\n<td>Modus<\/td>\n<td>Nilai yang paling sering muncul<\/td>\n<td>Menunjukkan data yang paling populer<\/td>\n<\/tr>\n<tr>\n<td>Jangkauan (Range)<\/td>\n<td>Selisih nilai terbesar dan terkecil<\/td>\n<td>Menunjukkan sebaran data<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<hr \/>\n<h2>Mean (Rata-rata): Jumlah Data Dibagi Banyak Data<\/h2>\n<p class=\"ds-markdown-paragraph\">Mean adalah ukuran pemusatan yang paling umum digunakan. Mean dihitung dengan menjumlahkan semua nilai data, kemudian dibagi dengan banyaknya data. Berikut penjelasan singkat sebelum masuk ke rumus:<\/p>\n<p class=\"ds-markdown-paragraph\"><em>Mean sering disebut &#8220;rata-rata&#8221; dan dilambangkan dengan x\u0304 (dibaca &#8220;x bar&#8221;). Rumus dasarnya sederhana: jumlahkan semua angka, lalu bagi dengan berapa banyak angka yang dijumlahkan.<\/em><\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Rumus mean untuk data tunggal:<\/strong><\/p>\n<div class=\"md-code-block md-code-block-light\">\n<div class=\"md-code-block-banner-wrap\">\n<div class=\"md-code-block-banner md-code-block-banner-lite\">\n<div class=\"_121d384\">\n<div class=\"d2a24f03\"><span class=\"d813de27\">text<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<pre>Mean (x\u0304) = (Jumlah semua data) \/ (Banyak data) = (\u2211 x\u1d62) \/ n<\/pre>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh:<\/strong>\u00a0Data: 5, 7, 8, 6, 4<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Jumlah = 5 + 7 + 8 + 6 + 4 = 30<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">n = 5<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Mean = 30 \u00f7 5 = 6<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Rumus mean untuk data berkelompok (tabel frekuensi):<\/strong><\/p>\n<div class=\"md-code-block md-code-block-light\">\n<div class=\"md-code-block-banner-wrap\">\n<div class=\"md-code-block-banner md-code-block-banner-lite\">\n<div class=\"_121d384\">\n<div class=\"d2a24f03\"><span class=\"d813de27\">text<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<pre>Mean = (\u2211 (x\u1d62 \u00d7 f\u1d62)) \/ (\u2211 f\u1d62)<\/pre>\n<\/div>\n<p class=\"ds-markdown-paragraph\">dengan x\u1d62 = nilai data, f\u1d62 = frekuensi.<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh data berkelompok:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Nilai (x\u1d62)<\/th>\n<th>Frekuensi (f\u1d62)<\/th>\n<th>x\u1d62 \u00d7 f\u1d62<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>5<\/td>\n<td>2<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>3<\/td>\n<td>18<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>4<\/td>\n<td>28<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>1<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td><strong>Jumlah<\/strong><\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>64<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Mean = 64 \u00f7 10 = 6,4<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Mencari nilai yang hilang jika mean diketahui:<\/strong><br \/>\nJika mean dari n data diketahui, maka:<\/p>\n<div class=\"md-code-block md-code-block-light\">\n<div class=\"md-code-block-banner-wrap\">\n<div class=\"md-code-block-banner md-code-block-banner-lite\">\n<div class=\"_121d384\">\n<div class=\"d2a24f03\"><span class=\"d813de27\">text<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<pre>Jumlah total = mean \u00d7 n\r\nNilai yang dicari = jumlah total - jumlah data yang diketahui<\/pre>\n<\/div>\n<hr \/>\n<h2>Median (Nilai Tengah): Data Harus Diurutkan Terlebih Dahulu<\/h2>\n<p class=\"ds-markdown-paragraph\">Median adalah nilai tengah dari data yang telah diurutkan dari terkecil ke terbesar. Berbeda dengan mean, median tidak terpengaruh oleh nilai ekstrem (pencilan). Berikut langkah-langkahnya:<\/p>\n<p class=\"ds-markdown-paragraph\">*Langkah 1: Urutkan data dari nilai terkecil ke terbesar. Langkah 2: Tentukan apakah banyak data (n) ganjil atau genap. Langkah 3: Jika n ganjil, median adalah data ke-(n+1)\/2. Jika n genap, median adalah rata-rata data ke-(n\/2) dan data ke-(n\/2 + 1).*<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Rumus median:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Banyak Data (n)<\/th>\n<th>Rumus Median<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Ganjil<\/td>\n<td>Data ke-(n+1)\/2<\/td>\n<\/tr>\n<tr>\n<td>Genap<\/td>\n<td>(Data ke-n\/2 + Data ke-(n\/2 + 1)) \/ 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh n ganjil:<\/strong>\u00a0Data: 4, 6, 7, 8, 10<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Urutan: 4, 6, 7, 8, 10<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">n = 5 (ganjil) \u2192 median = data ke-3 = 7<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh n genap:<\/strong>\u00a0Data: 4, 6, 7, 9<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Urutan: 4, 6, 7, 9<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">n = 4 (genap) \u2192 median = (data ke-2 + data ke-3) \/ 2 = (6 + 7) \/ 2 = 6,5<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Median untuk data berkelompok (tabel frekuensi):<\/strong><\/p>\n<ol start=\"1\">\n<li>\n<p class=\"ds-markdown-paragraph\">Tentukan letak median = (n+1)\/2<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Cari kelas yang mengandung median dengan menjumlahkan frekuensi kumulatif<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Gunakan rumus interpolasi (jika diperlukan)<\/p>\n<\/li>\n<\/ol>\n<hr \/>\n<h2>Modus: Nilai yang Paling Sering Muncul<\/h2>\n<p class=\"ds-markdown-paragraph\">Modus adalah nilai yang memiliki frekuensi tertinggi (paling sering muncul). Berbeda dengan mean dan median, modus dapat digunakan untuk data kategorik (bukan hanya numerik). Berikut penjelasannya:<\/p>\n<p class=\"ds-markdown-paragraph\"><em>Sebuah data bisa memiliki satu modus (unimodal), dua modus (bimodal), lebih dari dua modus (multimodal), atau tidak memiliki modus jika semua nilai muncul dengan frekuensi yang sama.<\/em><\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh mencari modus:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Data<\/th>\n<th>Frekuensi<\/th>\n<th>Keterangan<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>4<\/td>\n<td>1<\/td>\n<td>Muncul 1 kali<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>2<\/td>\n<td>Muncul 2 kali<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>1<\/td>\n<td>Muncul 1 kali<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>3<\/td>\n<td>Muncul 3 kali (tertinggi)<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>1<\/td>\n<td>Muncul 1 kali<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Modus = 7<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh data dengan dua modus (bimodal):<\/strong>\u00a03, 3, 4, 5, 5, 6<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">3 muncul 2 kali, 5 muncul 2 kali \u2192 modus = 3 dan 5<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh data tanpa modus:<\/strong>\u00a01, 2, 3, 4, 5<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Semua muncul 1 kali \u2192 tidak ada modus<\/p>\n<\/li>\n<\/ul>\n<hr \/>\n<h2>Jangkauan (Range): Selisih Nilai Terbesar dan Terkecil<\/h2>\n<p class=\"ds-markdown-paragraph\">Jangkauan adalah ukuran penyebaran data yang paling sederhana. Jangkauan menunjukkan seberapa jauh jarak antara nilai tertinggi dan nilai terendah dalam kumpulan data. Berikut rumusnya:<\/p>\n<p class=\"ds-markdown-paragraph\"><em>Jangkauan hanya memperhatikan dua nilai ekstrem (terbesar dan terkecil), sehingga tidak memberikan informasi tentang sebaran data di antaranya.<\/em><\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Rumus jangkauan:<\/strong><\/p>\n<div class=\"md-code-block md-code-block-light\">\n<div class=\"md-code-block-banner-wrap\">\n<div class=\"md-code-block-banner md-code-block-banner-lite\">\n<div class=\"_121d384\">\n<div class=\"d2a24f03\"><span class=\"d813de27\">text<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<pre>Jangkauan = Nilai maksimum - Nilai minimum<\/pre>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh:<\/strong>\u00a0Data: 4, 7, 9, 12, 15<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Nilai maksimum = 15<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Nilai minimum = 4<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Jangkauan = 15 &#8211; 4 = 11<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Contoh dari tabel:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Bulan<\/th>\n<th>Penjualan<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Jan<\/td>\n<td>120<\/td>\n<\/tr>\n<tr>\n<td>Feb<\/td>\n<td>135<\/td>\n<\/tr>\n<tr>\n<td>Mar<\/td>\n<td>110<\/td>\n<\/tr>\n<tr>\n<td>Apr<\/td>\n<td>140<\/td>\n<\/tr>\n<tr>\n<td>Mei<\/td>\n<td>155<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Jangkauan = 155 &#8211; 110 = 45<\/p>\n<hr \/>\n<h2>Strategi Menyelesaikan Soal Mean, Median, Modus, Jangkauan Tipe TKA<\/h2>\n<p class=\"ds-markdown-paragraph\">Agar tidak kebingungan saat mengerjakan soal TKA, ikuti langkah-langkah sistematis berikut:<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Langkah umum:<\/strong><\/p>\n<ol start=\"1\">\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Urutkan data<\/strong>\u00a0(terutama untuk mencari median dan jangkauan)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Hitung jumlah data dan banyaknya data<\/strong><\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Gunakan rumus yang sesuai<\/strong>\u00a0(mean, median, modus, jangkauan)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Untuk soal menaksir nilai yang tidak diketahui<\/strong>, gunakan persamaan mean<\/p>\n<\/li>\n<\/ol>\n<p class=\"ds-markdown-paragraph\"><strong>Trik khusus untuk berbagai tipe soal:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Tipe Soal<\/th>\n<th>Trik Cepat<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Mean data tunggal<\/td>\n<td>Jumlah \u00f7 n<\/td>\n<\/tr>\n<tr>\n<td>Mean data berfrekuensi<\/td>\n<td>\u03a3(x \u00d7 f) \u00f7 \u03a3f<\/td>\n<\/tr>\n<tr>\n<td>Median data tunggal<\/td>\n<td>Urutkan, cari tengah<\/td>\n<\/tr>\n<tr>\n<td>Median data berfrekuensi<\/td>\n<td>Hitung frekuensi kumulatif<\/td>\n<\/tr>\n<tr>\n<td>Modus<\/td>\n<td>Cari frekuensi tertinggi<\/td>\n<\/tr>\n<tr>\n<td>Jangkauan<\/td>\n<td>Maks &#8211; min<\/td>\n<\/tr>\n<tr>\n<td>Mencari nilai hilang dari mean<\/td>\n<td>(mean \u00d7 n) &#8211; jumlah diketahui<\/td>\n<\/tr>\n<tr>\n<td>Soal rata-rata dengan komposisi<\/td>\n<td>Buat sistem persamaan linear<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Trik khusus untuk soal rata-rata telur (dari file asli):<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Soal: Rata-rata berat telur kecil = 45g, sedang = 55g, besar = 65g. Setiap kemasan berisi 10 butir dengan rata-rata 55g. Kombinasi telur yang mungkin?<\/p>\n<p class=\"ds-markdown-paragraph\">Pendekatan:<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Misal a = jumlah telur kecil, b = sedang, c = besar<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">a + b + c = 10<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">(45a + 55b + 65c)\/10 = 55 \u2192 45a + 55b + 65c = 550<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Sederhanakan: bagi 5 \u2192 9a + 11b + 13c = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Substitusi c = 10 &#8211; a &#8211; b \u2192 9a + 11b + 13(10 &#8211; a &#8211; b) = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">9a + 11b + 130 &#8211; 13a &#8211; 13b = 110 \u2192 -4a &#8211; 2b + 130 = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">-4a &#8211; 2b = -20 \u2192 4a + 2b = 20 \u2192 2a + b = 10<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Cari pasangan (a,b) bilangan bulat tidak negatif dengan a + b \u2264 10<\/p>\n<\/li>\n<\/ul>\n<hr \/>\n<h2>Contoh Soal dan Pembahasan (Tipe TKA)<\/h2>\n<p class=\"ds-markdown-paragraph\">Berikut adalah contoh-contoh soal yang sering muncul dalam TKA Matematika SMP, lengkap dengan pembahasan langkah demi langkah.<\/p>\n<h3>Contoh 1: Soal Asli File (Rata-rata Telur)<\/h3>\n<p class=\"ds-markdown-paragraph\">Rata-rata berat telur kecil 45g, sedang 55g, besar 65g. Setiap kemasan berisi 10 butir dengan rata-rata 55g. Kombinasi telur yang mungkin adalah \u2026.<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Tentukan variabel.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">a = jumlah telur kecil (45g)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">b = jumlah telur sedang (55g)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">c = jumlah telur besar (65g)<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Buat persamaan.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">a + b + c = 10<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">(45a + 55b + 65c)\/10 = 55 \u2192 45a + 55b + 65c = 550<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Sederhanakan persamaan kedua.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Bagi kedua ruas dengan 5: 9a + 11b + 13c = 110<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 4: Substitusi c = 10 &#8211; a &#8211; b.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">9a + 11b + 13(10 &#8211; a &#8211; b) = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">9a + 11b + 130 &#8211; 13a &#8211; 13b = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">-4a &#8211; 2b + 130 = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">-4a &#8211; 2b = -20<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">4a + 2b = 20<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">2a + b = 10<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 5: Cari kemungkinan pasangan (a,b) dengan a,b \u2265 0 dan a+b \u2264 10.<\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>a<\/th>\n<th>b = 10 &#8211; 2a<\/th>\n<th>c = 10 &#8211; a &#8211; b<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>10<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>8<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>6<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>0<\/td>\n<td>5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: Salah satu kemungkinan adalah 1 telur besar dan 1 telur kecil (a=1, b=8, c=1)<\/strong><\/p>\n<hr \/>\n<h3>Contoh 2: Mean dari Data Tunggal<\/h3>\n<p class=\"ds-markdown-paragraph\">Data nilai ulangan matematika: 7, 8, 6, 9, 7, 8, 8, 10. Tentukan mean!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Jumlahkan semua data.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">7 + 8 + 6 + 9 + 7 + 8 + 8 + 10 = 63<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Hitung banyak data.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">n = 8<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Hitung mean.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Mean = 63 \u00f7 8 = 7,875<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 7,875<\/strong><\/p>\n<hr \/>\n<h3>Contoh 3: Median dari Data Ganjil<\/h3>\n<p class=\"ds-markdown-paragraph\">Data: 12, 15, 10, 13, 14. Tentukan median!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Urutkan data.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">10, 12, 13, 14, 15<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: n = 5 (ganjil).<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Median = data ke-(5+1)\/2 = data ke-3 = 13<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 13<\/strong><\/p>\n<hr \/>\n<h3>Contoh 4: Median dari Data Genap<\/h3>\n<p class=\"ds-markdown-paragraph\">Data: 8, 5, 9, 6, 7, 10. Tentukan median!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Urutkan data.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">5, 6, 7, 8, 9, 10<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: n = 6 (genap).<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Median = (data ke-3 + data ke-4) \u00f7 2 = (7 + 8) \u00f7 2 = 7,5<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 7,5<\/strong><\/p>\n<hr \/>\n<h3>Contoh 5: Modus dari Data Tunggal<\/h3>\n<p class=\"ds-markdown-paragraph\">Data: 4, 5, 5, 6, 7, 7, 7, 8, 9. Tentukan modus!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Hitung frekuensi setiap nilai.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">4: 1 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">5: 2 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">6: 1 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">7: 3 kali (tertinggi)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">8: 1 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">9: 1 kali<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Modus = nilai dengan frekuensi tertinggi = 7<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 7<\/strong><\/p>\n<hr \/>\n<h3>Contoh 6: Modus dari Data dengan Dua Modus (Bimodal)<\/h3>\n<p class=\"ds-markdown-paragraph\">Data: 3, 3, 4, 5, 5, 6. Tentukan modus!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">3 muncul 2 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">4 muncul 1 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">5 muncul 2 kali<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">6 muncul 1 kali<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Frekuensi tertinggi = 2, dicapai oleh nilai 3 dan 5.<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 3 dan 5<\/strong><\/p>\n<hr \/>\n<h3>Contoh 7: Jangkauan (Range)<\/h3>\n<p class=\"ds-markdown-paragraph\">Data: 23, 27, 25, 29, 24, 30, 22. Tentukan jangkauan!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Nilai terbesar = 30<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Nilai terkecil = 22<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Jangkauan = 30 &#8211; 22 = 8<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 8<\/strong><\/p>\n<hr \/>\n<h3>Contoh 8: Mencari Nilai Hilang jika Mean Diketahui<\/h3>\n<p class=\"ds-markdown-paragraph\">Rata-rata nilai 5 siswa adalah 80. Jika nilai 4 siswa adalah 75, 85, 90, 70, berapa nilai siswa ke-5?<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Hitung jumlah total.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Jumlah total = mean \u00d7 n = 80 \u00d7 5 = 400<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Hitung jumlah 4 siswa.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">75 + 85 + 90 + 70 = 320<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Hitung nilai siswa ke-5.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">400 &#8211; 320 = 80<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 80<\/strong><\/p>\n<hr \/>\n<h3>Contoh 9: Mean dari Data Berfrekuensi (Tabel)<\/h3>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Nilai<\/th>\n<th>Frekuensi<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>5<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Tentukan mean!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Nilai (x)<\/th>\n<th>Frekuensi (f)<\/th>\n<th>x \u00d7 f<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>5<\/td>\n<td>2<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>3<\/td>\n<td>18<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>4<\/td>\n<td>28<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>1<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td><strong>Jumlah<\/strong><\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>64<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Mean = 64 \u00f7 10 = 6,4<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 6,4<\/strong><\/p>\n<hr \/>\n<h3>Contoh 10: Median dari Data Berfrekuensi<\/h3>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Nilai<\/th>\n<th>Frekuensi<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>4<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Tentukan median!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Total frekuensi = 1 + 3 + 2 + 4 = 10 (genap)<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Median = (data ke-5 + data ke-6) \u00f7 2<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Tentukan data ke-5 dan ke-6.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Urutan: 4, 5,5,5, 6,6, 7,7,7,7<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Data ke-5 = 6<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Data ke-6 = 6<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Median = (6 + 6) \u00f7 2 = 6<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 6<\/strong><\/p>\n<hr \/>\n<h3>Contoh 11: Soal Cerita Rata-rata Target<\/h3>\n<p class=\"ds-markdown-paragraph\">Sebuah toko menginginkan rata-rata penjualan 5 hari adalah 50 unit. Penjualan 4 hari pertama: 45, 55, 40, 60. Berapa penjualan hari ke-5 yang harus dicapai?<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Jumlah target = 50 \u00d7 5 = 250 unit<\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Jumlah 4 hari = 45 + 55 + 40 + 60 = 200 unit<\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Hari ke-5 = 250 &#8211; 200 = 50 unit<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 50 unit<\/strong><\/p>\n<hr \/>\n<h3>Contoh 12: Jangkauan dari Data Tabel<\/h3>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Bulan<\/th>\n<th>Penjualan<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Jan<\/td>\n<td>120<\/td>\n<\/tr>\n<tr>\n<td>Feb<\/td>\n<td>135<\/td>\n<\/tr>\n<tr>\n<td>Mar<\/td>\n<td>110<\/td>\n<\/tr>\n<tr>\n<td>Apr<\/td>\n<td>140<\/td>\n<\/tr>\n<tr>\n<td>Mei<\/td>\n<td>155<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Tentukan jangkauan!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Maksimum = 155<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Minimum = 110<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Jangkauan = 155 &#8211; 110 = 45<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 45<\/strong><\/p>\n<hr \/>\n<h3>Contoh 13: Mencari Nilai x dari Median<\/h3>\n<p class=\"ds-markdown-paragraph\">Median data: 5, 7, 4, 8, 6, x adalah 6,5. Tentukan nilai x!<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Urutkan data (dengan x belum diketahui).<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Tanpa x: 4, 5, 6, 7, 8<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Median = 6,5 \u2192 ini adalah rata-rata dua data tengah<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Karena n = 6 (genap), median = (data ke-3 + data ke-4) \u00f7 2 = 6,5<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">(data ke-3 + data ke-4) = 13<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Kemungkinan posisi x.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Jika x &gt; 6, urutan: 4,5,6,7,8,x \u2192 data ke-3=6, data ke-4=7 \u2192 (6+7)\/2=6,5 (cocok)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Maka x bisa lebih besar dari 8, atau x = 7? Jika x=7, urutan: 4,5,6,7,7,8 \u2192 data ke-3=6, ke-4=7 \u2192 (6+7)\/2=6,5 (cocok)<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: x \u2265 7 (atau x &gt; 6)<\/strong><\/p>\n<hr \/>\n<h3>Contoh 14: Soal Rata-rata dengan Penambahan Data<\/h3>\n<p class=\"ds-markdown-paragraph\">Rata-rata berat 5 butir telur adalah 50 gram. Jika ditambah satu butir telur, rata-ratanya menjadi 52 gram. Berapa berat telur yang ditambahkan?<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Jumlah awal = 50 \u00d7 5 = 250 gram<\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Jumlah setelah ditambah = 52 \u00d7 6 = 312 gram<\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Berat telur tambahan = 312 &#8211; 250 = 62 gram<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: 62 gram<\/strong><\/p>\n<hr \/>\n<h3>Contoh 15: Soal Rata-rata Berdasarkan Kelompok<\/h3>\n<p class=\"ds-markdown-paragraph\">Sebuah kelas terdiri dari 20 siswa. Rata-rata nilai matematika siswa laki-laki 75, siswa perempuan 85. Jika rata-rata seluruh siswa 80, berapa jumlah siswa laki-laki dan perempuan?<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Pembahasan:<\/strong><\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 1: Misalkan L = jumlah laki-laki, P = jumlah perempuan.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">L + P = 20<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 2: Jumlah nilai total = (75 \u00d7 L) + (85 \u00d7 P)<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">Rata-rata total = 80 \u2192 jumlah total = 80 \u00d7 20 = 1.600<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Langkah 3: Persamaan: 75L + 85P = 1.600<\/p>\n<p class=\"ds-markdown-paragraph\">Langkah 4: Substitusi P = 20 &#8211; L.<\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\">75L + 85(20 &#8211; L) = 1.600<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">75L + 1.700 &#8211; 85L = 1.600<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">-10L + 1.700 = 1.600<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">-10L = -100<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">L = 10, P = 10<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\"><strong>Jawaban: Laki-laki = 10, Perempuan = 10<\/strong><\/p>\n<hr \/>\n<h2>Latihan Mandiri untuk Menguji Pemahaman<\/h2>\n<p class=\"ds-markdown-paragraph\">Kerjakan soal-soal berikut dengan menerapkan strategi yang sudah dipelajari.<\/p>\n<ol start=\"1\">\n<li>\n<p class=\"ds-markdown-paragraph\">Data: 8, 10, 7, 9, 11, 8, 12. Tentukan mean, median, modus, dan jangkauan!<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Rata-rata nilai 6 siswa adalah 85. Jika 5 siswa nilainya 80, 90, 85, 75, 95, berapa nilai siswa ke-6?<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Data: 15, 18, 16, 20, 17, 15, 19, 16. Tentukan median dan modus!<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Sebuah kemasan berisi 10 butir telur. Rata-rata berat per telur harus 55 gram. Tersedia telur kecil (45g), sedang (55g), besar (65g). Tentukan 3 kemungkinan kombinasi telur!<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Data frekuensi:<\/p>\n<\/li>\n<\/ol>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Nilai<\/th>\n<th>Frekuensi<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>3<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\">Tentukan mean dan median!<\/p>\n<ol start=\"6\">\n<li>\n<p class=\"ds-markdown-paragraph\">Nilai ulangan: 6, 7, 8, 6, 9, 8, 7, 6, 8, 9. Tentukan modus!<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Jangkauan data 12, 15, a, 18, 14 adalah 8. Tentukan nilai a yang mungkin!<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">(Tipe TKA) Rata-rata berat 5 butir telur adalah 50 gram. Jika ditambah satu butir telur, rata-ratanya menjadi 52 gram. Berapa berat telur yang ditambahkan?<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Median data: 5, 7, 4, 8, 6, x adalah 6,5. Tentukan nilai x!<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Sebuah kelas terdiri dari 20 siswa. Rata-rata nilai matematika siswa laki-laki 75, siswa perempuan 85. Jika rata-rata seluruh siswa 80, berapa jumlah siswa laki-laki dan perempuan?<\/p>\n<\/li>\n<\/ol>\n<p class=\"ds-markdown-paragraph\"><strong>Kunci Jawaban:<\/strong><\/p>\n<ol start=\"1\">\n<li>\n<p class=\"ds-markdown-paragraph\">Mean = 9,29; Median = 8; Modus = 8; Jangkauan = 5<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">85<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Median = (16+17)\/2 = 16,5; Modus = 15 dan 16 (bimodal)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">(0,10,0), (1,8,1), (2,6,2), (3,4,3), (4,2,4), (5,0,5)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Mean = 4,85; Median = 5<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Modus = 6 dan 8 (bimodal)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">a = 8 atau a = 20 (karena jangkauan = 8)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">62 gram<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">x \u2265 7<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Laki-laki = 10, Perempuan = 10<\/p>\n<\/li>\n<\/ol>\n<hr \/>\n<h2>Kesalahan Umum dalam Mean, Median, Modus, Jangkauan<\/h2>\n<p class=\"ds-markdown-paragraph\">Berikut adalah kesalahan yang paling sering dilakukan siswa beserta cara memperbaikinya:<\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Kesalahan<\/th>\n<th>Contoh<\/th>\n<th>Perbaikan<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Lupa mengurutkan data untuk median<\/td>\n<td>Data: 8,5,7 \u2192 median = 7 \u274c<\/td>\n<td>Urutkan: 5,7,8 \u2192 median = 7 \u2713<\/td>\n<\/tr>\n<tr>\n<td>Keliru rumus median untuk n genap<\/td>\n<td>Hanya mengambil data ke-n\/2 saja \u274c<\/td>\n<td>Rata-rata dua data tengah \u2713<\/td>\n<\/tr>\n<tr>\n<td>Modus dianggap selalu ada<\/td>\n<td>Semua data muncul sekali, dipaksakan ada modus<\/td>\n<td>Tidak ada modus<\/td>\n<\/tr>\n<tr>\n<td>Jangkauan salah hitung<\/td>\n<td>Maks &#8211; min = nilai tengah \u274c<\/td>\n<td>Maks &#8211; min = jangkauan \u2713<\/td>\n<\/tr>\n<tr>\n<td>Keliru menentukan posisi median untuk data genap<\/td>\n<td>Mengambil data ke-5 dari 10 data<\/td>\n<td>Ambil data ke-5 dan ke-6<\/td>\n<\/tr>\n<tr>\n<td>Salah dalam perhitungan mean berfrekuensi<\/td>\n<td>Lupa mengalikan nilai dengan frekuensi<\/td>\n<td>\u03a3(x \u00d7 f) \u00f7 \u03a3f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<hr \/>\n<h2>Ringkasan Rumus Penting<\/h2>\n<p class=\"ds-markdown-paragraph\"><strong>Tabel ringkasan rumus mean, median, modus, jangkauan:<\/strong><\/p>\n<div class=\"ds-scroll-area ds-scroll-area--show-on-focus-within _1210dd7 c03cafe9\">\n<div class=\"ds-scroll-area__gutters\">\n<div class=\"ds-scroll-area__horizontal-gutter\"><\/div>\n<div class=\"ds-scroll-area__vertical-gutter\"><\/div>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>Ukuran<\/th>\n<th>Rumus\/Cara<\/th>\n<th>Keterangan<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Mean (data tunggal)<\/td>\n<td>x\u0304 = \u03a3x\u1d62 \/ n<\/td>\n<td>Jumlah semua \u00f7 banyak data<\/td>\n<\/tr>\n<tr>\n<td>Mean (data berfrekuensi)<\/td>\n<td>x\u0304 = \u03a3(x\u1d62 \u00d7 f\u1d62) \/ \u03a3f\u1d62<\/td>\n<td>Nilai \u00d7 frekuensi<\/td>\n<\/tr>\n<tr>\n<td>Median (n ganjil)<\/td>\n<td>Data ke-(n+1)\/2<\/td>\n<td>Setelah diurutkan<\/td>\n<\/tr>\n<tr>\n<td>Median (n genap)<\/td>\n<td>(data ke-n\/2 + data ke-(n\/2+1)) \/ 2<\/td>\n<td>Setelah diurutkan<\/td>\n<\/tr>\n<tr>\n<td>Modus<\/td>\n<td>Nilai dengan frekuensi tertinggi<\/td>\n<td>Bisa lebih dari satu<\/td>\n<\/tr>\n<tr>\n<td>Jangkauan<\/td>\n<td>Nilai maksimum &#8211; nilai minimum<\/td>\n<td>&#8211;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Rumus mencari nilai hilang dari mean:<\/strong><\/p>\n<div class=\"md-code-block md-code-block-light\">\n<div class=\"md-code-block-banner-wrap\">\n<div class=\"md-code-block-banner md-code-block-banner-lite\">\n<div class=\"_121d384\">\n<div class=\"d2a24f03\"><span class=\"d813de27\">text<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<pre>Nilai yang dicari = (mean \u00d7 n) - (jumlah data yang diketahui)<\/pre>\n<\/div>\n<p class=\"ds-markdown-paragraph\"><strong>Rumus rata-rata gabungan:<\/strong><\/p>\n<div class=\"md-code-block md-code-block-light\">\n<div class=\"md-code-block-banner-wrap\">\n<div class=\"md-code-block-banner md-code-block-banner-lite\">\n<div class=\"_121d384\">\n<div class=\"d2a24f03\"><span class=\"d813de27\">text<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<pre>x\u0304_gabungan = (n\u2081 \u00d7 x\u0304\u2081 + n\u2082 \u00d7 x\u0304\u2082) \/ (n\u2081 + n\u2082)<\/pre>\n<\/div>\n<hr \/>\n<h2>Kesimpulan: Kuasai Mean, Median, Modus, Jangkauan untuk Raih Skor Maksimal<\/h2>\n<p class=\"ds-markdown-paragraph\">Untuk menguasai kompetensi penentuan dan penaksiran rerata (mean), median, modus, dan jangkauan (range) dari data dalam TKA Matematika SMP, ingatlah poin-poin penting berikut:<\/p>\n<p class=\"ds-markdown-paragraph\"><strong>Empat pilar utama statistika deskriptif:<\/strong><\/p>\n<ol start=\"1\">\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Mean = jumlah semua data \u00f7 banyak data<\/strong>\u00a0\u2013 paling umum digunakan, tetapi sensitif terhadap nilai ekstrem<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Median = nilai tengah setelah diurutkan<\/strong>\u00a0\u2013 tahan terhadap nilai ekstrem, cocok untuk data dengan pencilan<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Modus = nilai yang paling sering muncul<\/strong>\u00a0\u2013 berguna untuk data kategorik<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Jangkauan = nilai maksimum &#8211; nilai minimum<\/strong>\u00a0\u2013 ukuran penyebaran paling sederhana<\/p>\n<\/li>\n<\/ol>\n<p class=\"ds-markdown-paragraph\"><strong>Langkah penyelesaian yang sistematis:<\/strong><\/p>\n<ol start=\"1\">\n<li>\n<p class=\"ds-markdown-paragraph\">Urutkan data (untuk median dan jangkauan)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Hitung jumlah data dan banyaknya data<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Gunakan rumus yang sesuai<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\">Untuk soal rata-rata dengan komposisi (seperti telur), buat sistem persamaan linear<\/p>\n<\/li>\n<\/ol>\n<p class=\"ds-markdown-paragraph\"><strong>Tips menghafal:<\/strong><\/p>\n<ul>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Mean<\/strong>\u00a0\u2192 &#8220;Me-an&#8221; = jumlah dibagi banyak<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Median<\/strong>\u00a0\u2192 &#8220;Medi-an&#8221; = nilai tengah (medium)<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Modus<\/strong>\u00a0\u2192 &#8220;Modus&#8221; = mode = yang paling sering muncul<\/p>\n<\/li>\n<li>\n<p class=\"ds-markdown-paragraph\"><strong>Jangkauan<\/strong>\u00a0\u2192 &#8220;Range&#8221; = dari terkecil ke terbesar<\/p>\n<\/li>\n<\/ul>\n<p class=\"ds-markdown-paragraph\">Dengan menguasai mean, median, modus, dan jangkauan, siswa tidak hanya siap menghadapi TKA Matematika SMP, tetapi juga mampu menganalisis data dalam kehidupan sehari-hari, seperti menentukan nilai rata-rata rapor, mengetahui produk terlaris, atau memahami sebaran nilai ujian. Terus berlatih, dan jadikan statistika sebagai alat bantu yang powerful.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bimbel Rumah Pintar &#8211; Pernahkah Anda bertanya-tanya bagaimana cara menentukan nilai rata-rata rapor? Atau bagaimana toko menentukan produk terlaris? Atau bagaimana guru mengetahui nilai tengah dari hasil ujian? Semua ini melibatkan konsep apa itu mean (rerata), median, modus, dan jangkauan [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2177,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[36],"tags":[247,244,245,246,248,207],"class_list":["post-2175","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-konsep-dan-pelajaran","tag-jangkauan","tag-mean","tag-median","tag-modus","tag-statistika-smp","tag-tka-matematika-smp"],"_links":{"self":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts\/2175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/comments?post=2175"}],"version-history":[{"count":1,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts\/2175\/revisions"}],"predecessor-version":[{"id":2181,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts\/2175\/revisions\/2181"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/media\/2177"}],"wp:attachment":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/media?parent=2175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/categories?post=2175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/tags?post=2175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}