Artikel Matematika kelas 8 ini membahas mengenai pengertian ukuran pemusatan data, yang meliputi mean, median, modus, cara menentukan nilai mean, median, modus, dan masing-masing contoh soalnya.
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Banyak orang suka menyembunyikan nilai ujiannya supaya orang lain nggak tau, seakan-akan nilai ujian tuhh rahasiaaa banget.
Pernah nggak sih temenmu nanya nilai ujian yang udah kamu rahasiakan banget? Terus pada akhirnya, kamu kasih tau dengan harapan dia nyebutin nilainya juga. Eh, ternyata dia ikut ujian susulan, jadi nilainya belum keluar deh.
Mungkin, kamu dan yang lain ngerasa, “nggak adil banget sih, kan dia udah tau nilai kita semua” atau “yahh… kalo kita nanya nilainya, pasti nggak bakal dikasih tau nih”.
Padahal, kamu bisa tau nilainya loh, tapi dengan syarat, kamu harus tau nilai rata-rata kelas. Tenang, nanti bakal aku lanjut bahas caranya. Nah, ngomongin tentang rata-rata, sebenarnya menghitung nilai rata-rata udah pernah dipelajari waktu SD dulu. Di SMP ini, kamu bakal belajar yang sedikit lebih kompleks, tapi tetap seru kok!
Rata-rata (mean) termasuk salah satu contoh ukuran pemusatan data. Hah, apa itu ukuran pemusatan data?
Pengertian ukuran pemusatan data adalah sembarang ukuran yang menjadi pusat dari beberapa data, dengan syarat data-data ini sudah diurutkan dari yang terkecil ke terbesar, atau sebaliknya. Simpelnya, dari beberapa data terurut, akan diperoleh suatu nilai yang menjadi nilai pusat atau perwakilannya.
Sebenarnya, ukuran pemusatan data itu nggak cuma ada rata-rata (mean) aja. Ada beberapa contoh ukuran pemusatan data lain, seperti modus dan median. Kita akan bahas satu persatu tiga macam ukuran pemusatan data, dimulai dari rata-rata dulu, ya.
Mean (Rata-Rata)
Rata-rata bisa kita sebut juga dengan mean. Rata-rata (mean) adalah suatu bilangan yang mewakili sekumpulan data. Rata-rata (mean) dilambangkan dengan simbol x̄ (dibaca x bar).
Kita bisa menghitung nilai rata-rata atau mean dari data tunggal dan data tunggal berkelompok atau berfrekuensi. Apa ya bedanya data tunggal dan data tunggal berkelompok?
Jadi kalo data tunggal, kita mengumpulkan atau memperoleh data apa adanya (bisa berurutan atau acak) dan tidak mengelompokkannya ke tabel frekuensi. Contoh data tunggal:
Nilai Ujian Matematika kelas VIII-A
5 9 7 8 6 5
6 8 9 5 7 8
7 9 8 6 6 5
8 8 6 5 7 5
7 8 6 5 5 7
Angka 5,6,7,8,9 dari data di atas disebut datum atau bisa dibilang masing-masing angka yang ada pada suatu data.
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Cara Mencari Rata-Rata (Mean)
Untuk memperoleh nilai rata-rata, kita bisa membagi jumlah semua nilai atau datum-nya dengan banyaknya data. Nah, ini dia rumus mencari mean-nya:
Kebayang nggak sih gimana ribet dan panjangnya tulisan, kalo misalnya kamu harus ngumpulin nilai dari 200 orang? Nggak efisien banget dong. Solusinya, kita bisa mengelompokkan data atau nilainya dengan tabel frekuensi, atau bisa juga dibilang data tunggal berkelompok. Misalnya:
Nilai
5
6
7
8
9
Frekuensi
14
25
31
20
10
Untuk rumus mencari nilai rata-rata data tunggal berkelompok, bisa ditulis seperti ini:
Kita coba yuk latihan soal pakai rumus-rumus itu!
Contoh Soal Mencari Rata-Rata (Mean)
Data nilai ulangan harian IPA kelas VIII-1. Berapa banyak siswa di kelas itu yang nilainya lebih dari rata-rata?
Penyelesaian:
Cari dulu nilai rata-rata pakai rumus data tunggal berkelompok:
Diperoleh nilai rata-ratanya adalah 6,625. Karena yang ditanya di soal itu banyak siswa yang nilainya di atas rata-rata, maka nilainya ada 7 sampai 10. Kalau kita total semua jumlah siswanya, ada sebanyak 21 siswa.
Median (Data Tengah)
Data tengah atau median adalah datum yang letaknya di tengah suatu kumpulan data, tapi dengan syarat datanya sudah diurutkan dari yang terkecil sampai terbesar.
Median dapat dilambangkan dengan Me. Nah, kunci untuk mencari nilai median ini, kamu bisa perhatikan jumlah data yang ada, misal datanya itu ganjil atau genap. Karena, beda jumlah data, beda juga rumus mediannya.
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Cara Mencari Median
Seperti yang sudah disebutkan sebelumnya, untuk mencari nilai median, punya rumus yang berbeda. Setiap rumus ada perbedaannya, bergantung dari banyaknya data. Berikut rumus mencari median berdasarkan data ganjil dan data genap:
Untuk data berjumlah ganjil, kamu bisa langsung ambil angka tengahnya. Tapi, untuk data berjumlah genap, akan ada 2 angka yang ditengah. Jadi, supaya kamu bisa peroleh nilai mediannya, harus pakai rumus yang berbeda. Nah, kalo kamu masih bingung dan nggak kebayang pakai rumusnya, mendingan kita langsung bahas soal yuk!
Contoh Soal Mencari Median
Soal 1
Median dari data: 7, 8, 8, 9, 4, 3, 7, 9, 5, 7, 6, 5, 6 adalah …
Penyelesaian:
Ingat ! urutkan nilainya dari terkecil sampai terbesar
3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9 (n =13 termasuk data ganjil). Maka, kamu bisa menggunakan rumus median untuk data ganjil, yaitu:
Sehingga, diperoleh nilai mediannya adalah 7.
Soal 2
Median dari data berikut adalah …
Penyelesaian:
Kemudian, hitung dulu banyaknya data yang ada. Karena datanya genap, maka kamu bisa menggunakan rumus median untuk data genap, yaitu:
Jadi diperoleh nilai mediannya, yaitu 7.
Modus (Nilai yang Sering Muncul)
Nah, untuk macam ukuran pemusatan data yang ketiga ini, pasti udah nggak asing lagi, kan? Yap, modus adalah nilai yang paling sering muncul. Jadi, dalam kelompok data, jika ada angka yang paling banyak ada (paling sering muncul), itu lah yang dinamakan modus. Biasanya, modus dilambangkan dengan Mo.
Kalau data yang kamu peroleh merupakan data tunggal berkelompok atau data yang dikelompokkan ke dalam tabel, maka kamu bisa langsung lihat datum atau nilai dengan frekuensi paling tinggi. Tapi, kalo data tunggal biasa, kamu bisa gunakan tabel turus/ tally. Biar kamu paham kita ke contoh soal ya!
Contoh Soal Mencari Modus
Modus dari data berikut adalah:
102, 108, 106, 107, 108
105, 107, 105, 108, 106
106, 106, 107, 102, 105
105, 102, 106, 105, 106
107, 106, 105, 106, 102
105, 107, 107, 106, 105
106, 106, 105, 107, 102
Penyelesaian:
Nah, karena data di atas merupakan data tunggal biasa, agar lebih mudah, buat dalam bentuk tabel turus seperti ini:
Kemudian, kalau kita lihat, data yang paling sering muncul adalah 106 karena nilai frekuensinya paling tinggi, yaitu 11. Jadi, modus dari data itu adalah 106.
Nah, kita udah bahas 3 ukuran pemusatan data nih. Sesuai janji di awal, kita bakal bahas cara mencari nilai salah satu siswa jika diketahui rata-rata nilai kelasnya. Caranya itu mirip banget sama soal di bawah ini, jadi pahami ya!
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Wah, seru banget kan bahasan materi mean, median, dan modus ini. Soal-soal ukuran pemusatan data ini tuh bervariasi banget. Selain harus paham konsep, kamu juga harus terbiasa hitung cepat dan tepat.
Caranya gimana tuhh supaya bisa hitung cepat dan tepat? Kamu harus perbanyak latihan, nah makanya setelah baca artikel ini langsung aja asah pemahaman dan kemampuan hitung kamu di ruangbelajar. Soal-soalnya bagus banget dijadikan latihan dan bisa mempertajam pemahaman kamu. Selamat belajar!
Referensi:
Kurniawan, (2013) Mandiri Matematika Untuk Kelas SMP/MTs Kelas VIII. Jakarta: Erlangga.
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<h1 class="content-title">
Rumus dan Cara Menghitung Mean, Median, Modus | Matematika Kelas 8 </h1>
<div class="content-meta">
<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kak-efira-mt-saintek" class="">Kak Efira MT Saintek</a> </p>
<p class="content-info"><span>May 2, 2024 • </span> <span>6 minutes read</span></p>
<br />
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<p style="text-align: left;"><img fetchpriority="high" decoding="async" style="height: auto; max-width: 100%; width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/2958a14f-ffcb-4eb2-bf43-0a639d6ebcad.png" alt="rumus dan cara menghitung mean, median, modus" width="820" height="410" /></p>
<blockquote>
<p style="text-align: center; font-size: 16px;"><em><a style="font-weight: bold;" href="/blog/tag/matematika-viii" rel="noopener">Artikel Matematika kelas 8</a> ini membahas mengenai pengertian <span style="font-weight: bold;">ukuran pemusatan data</span>, yang meliputi </em><span style="font-weight: bold;">mean</span><em><span style="font-weight: bold;">, median, modus</span>, cara menentukan nilai </em>mean<em>, median, modus, dan masing-masing contoh soalnya.</em></p>
</blockquote>
<p style="text-align: center;"><em>—</em></p>
<p> </p>
<p style="text-align: justify;">Banyak orang suka menyembunyikan nilai ujiannya supaya orang lain nggak tau, seakan-akan nilai ujian tuhh rahasiaaa banget.</p>
<p style="text-align: justify;">Pernah nggak sih temenmu nanya nilai ujian yang udah kamu rahasiakan banget? Terus pada akhirnya, kamu kasih tau dengan harapan dia nyebutin nilainya juga. Eh, ternyata dia ikut ujian susulan, jadi nilainya belum keluar deh.</p>
<p style="text-align: justify;">Mungkin, kamu dan yang lain ngerasa, “nggak adil banget sih, kan dia udah tau nilai kita semua” atau “yahh… kalo kita nanya nilainya, pasti nggak bakal dikasih tau nih”.</p>
<p style="text-align: justify;">Padahal, kamu bisa tau nilainya loh, tapi dengan syarat, kamu harus tau nilai rata-rata kelas. Tenang, nanti bakal aku lanjut bahas caranya. Nah, ngomongin tentang rata-rata, sebenarnya <a style="font-weight: bold;" href="/blog/menghitung-mean-median-dan-modus" rel="noopener">menghitung nilai rata-rata udah </a><strong><a href="/blog/menghitung-mean-median-dan-modus" rel="noopener">pernah dipelajari waktu SD dulu</a>. </strong>Di SMP ini, kamu bakal belajar yang sedikit lebih kompleks, tapi tetap seru kok!</p>
<p style="text-align: justify;">Rata-rata (mean) termasuk salah satu contoh ukuran pemusatan data. Hah, apa itu ukuran pemusatan data?</p>
<p style="text-align: justify;"><span style="font-weight: bold;">Pengertian ukuran pemusatan data adalah</span> <span style="font-weight: bold;">sembarang ukuran yang menjadi pusat dari beberapa data</span>, dengan syarat data-data ini sudah diurutkan dari yang terkecil ke terbesar, atau sebaliknya. Simpelnya, dari beberapa data terurut, akan diperoleh suatu nilai yang menjadi nilai pusat atau perwakilannya.</p>
<p style="text-align: justify;">Sebenarnya, ukuran pemusatan data itu nggak cuma ada rata-rata (mean) aja. Ada beberapa contoh ukuran pemusatan data lain, seperti modus dan median. Kita akan bahas satu persatu <span style="font-weight: bold;">tiga macam ukuran pemusatan data</span>, dimulai dari rata-rata dulu, ya.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Mean (Rata-Rata)</span></h2>
<p style="text-align: justify;">Rata-rata bisa kita sebut juga dengan mean. <span style="font-weight: bold;">Rata-rata (mean) adalah suatu bilangan yang mewakili sekumpulan data</span>. Rata-rata (mean) dilambangkan dengan <span style="font-size: 16px;">simbol x̄</span><span style="font-size: 11px;"> <span style="font-size: 16px;">(</span></span>dibaca x bar).</p>
<p style="text-align: justify;">Kita bisa menghitung nilai rata-rata atau mean dari data tunggal dan data tunggal berkelompok atau berfrekuensi. Apa ya bedanya data tunggal dan data tunggal berkelompok?</p>
<p style="text-align: justify;">Jadi kalo data tunggal, kita mengumpulkan atau memperoleh data apa adanya (bisa berurutan atau acak) dan tidak mengelompokkannya ke tabel frekuensi. Contoh data tunggal:</p>
<p style="text-align: justify;"><strong>Nilai Ujian Matematika kelas VIII-A</strong></p>
<p style="text-align: justify;"><strong>5 9 7 8 6 5<br />
</strong><strong>6 8 9 5 7 8<br />
</strong><strong>7 9 8 6 6 5<br />
</strong><strong>8 8 6 5 7 5<br />
</strong><strong>7 8 6 5 5 7</strong></p>
<p style="text-align: justify;"><strong><br />
</strong>Angka 5,6,7,8,9 dari data di atas disebut datum atau bisa dibilang <strong>masing-masing angka yang ada pada suatu data. </strong></p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/blog/statistika-dan-diagram-penyajian-data" rel="noopener">Mengenal Statistika dalam Diagram Penyajian Data</a></strong></p>
<p> </p>
<h3><span style="font-size: 14pt;">Cara Mencari Rata-Rata (Mean)</span></h3>
<p style="text-align: justify;">Untuk memperoleh nilai rata-rata, kita bisa membagi jumlah semua nilai atau datum-nya dengan banyaknya data. Nah, ini dia <span style="font-weight: bold;">rumus mencari mean</span>-nya:</p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/9529cf8d-4cbf-43f2-a9a2-e3173bacfaa3.png" alt="rumus mencari nilai rata-rata data tunggal" width="600" height="400" /></p>
<p> </p>
<p style="text-align: justify;">Kebayang nggak sih gimana ribet dan panjangnya tulisan, kalo misalnya kamu harus ngumpulin nilai dari 200 orang? Nggak efisien banget dong. Solusinya, kita bisa mengelompokkan data atau nilainya dengan tabel frekuensi, atau bisa juga dibilang data tunggal berkelompok. Misalnya:</p>
<table style="border-collapse: collapse; table-layout: fixed; margin-left: auto; margin-right: auto; border: none; width: 420px;">
<tbody>
<tr>
<td style="border: 1pt solid #000000; width: 149px; padding: 4px;">
<p style="text-align: center;"><strong>Nilai</strong></p>
</td>
<td style="border: 1pt solid #000000; width: 49px; padding: 4px;">
<p style="text-align: center;">5</p>
</td>
<td style="border: 1pt solid #000000; width: 47px; padding: 4px;">
<p style="text-align: center;">6</p>
</td>
<td style="border: 1pt solid #000000; width: 46px; padding: 4px;">
<p style="text-align: center;">7</p>
</td>
<td style="border: 1pt solid #000000; width: 46px; padding: 4px;">
<p style="text-align: center;">8</p>
</td>
<td style="border: 1pt solid #000000; width: 82px; padding: 4px;">
<p style="text-align: center;">9</p>
</td>
</tr>
<tr>
<td style="border: 1pt solid #000000; width: 149px; padding: 4px;">
<p style="text-align: center;"><strong>Frekuensi</strong></p>
</td>
<td style="border: 1pt solid #000000; width: 49px; padding: 4px;">
<p style="text-align: center;">14</p>
</td>
<td style="border: 1pt solid #000000; width: 47px; padding: 4px;">
<p style="text-align: center;">25</p>
</td>
<td style="border: 1pt solid #000000; width: 46px; padding: 4px;">
<p style="text-align: center;">31</p>
</td>
<td style="border: 1pt solid #000000; width: 46px; padding: 4px;">
<p style="text-align: center;">20</p>
</td>
<td style="border: 1pt solid #000000; width: 82px; padding: 4px;">
<p style="text-align: center;">10</p>
</td>
</tr>
</tbody>
</table>
<p> </p>
<p>Untuk <span style="font-weight: bold;">rumus mencari nilai rata-rata data tunggal berkelompok</span>, bisa ditulis seperti ini:</p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/9e27ff72-9b6b-4376-8eba-f85de6ae83be.png" alt="rumus mencari nilai rata-rata tunggal berkelompok" width="600" height="400" /></p>
<p> </p>
<p style="text-align: justify;">Kita coba yuk latihan soal pakai rumus-rumus itu!</p>
<p> </p>
<h3><span style="font-size: 14pt;">Contoh Soal Mencari Rata-Rata (Mean)</span></h3>
<p style="text-align: justify;">Data nilai ulangan harian IPA kelas VIII-1. Berapa banyak siswa di kelas itu yang nilainya lebih dari rata-rata?</p>
<p><img decoding="async" style="width: 532px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-18-2021-12-37-32-71-PM.png" width="532" /></p>
<p> </p>
<p><span style="font-weight: bold;">Penyelesaian:</span></p>
<p>Cari dulu nilai rata-rata pakai rumus data tunggal berkelompok:</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-18-2021-12-38-44-23-PM.png" /></p>
<p style="text-align: justify;">Diperoleh nilai rata-ratanya adalah 6,625. Karena yang ditanya di soal itu banyak siswa yang nilainya di atas rata-rata, maka nilainya ada 7 sampai 10. Kalau kita total semua jumlah siswanya, ada sebanyak 21 siswa.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Median (Data Tengah)</span></h2>
<p style="text-align: justify;">Data tengah atau <span style="font-weight: bold;">median adalah datum yang letaknya di tengah suatu kumpulan data</span>, tapi dengan <strong>syarat datanya sudah diurutkan dari yang terkecil sampai terbesar.</strong></p>
<p style="text-align: justify;">Median dapat dilambangkan dengan Me. Nah, kunci untuk mencari nilai median ini, kamu bisa perhatikan jumlah data yang ada, misal datanya itu ganjil atau genap. Karena, beda jumlah data, beda juga rumus mediannya.</p>
<p><img loading="lazy" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/9851d5af-ea53-466a-b34b-2d259c7de4bb.png" alt="cara mencari median" width="600" height="900" /></p>
<p style="font-weight: bold;">Baca Juga: <a href="/blog/matematika-kelas-8-cara-menyelesaikan-sistem-persamaan-linear-dua-variabel-spldv" rel="noopener">Cara Menyelesaikan Sistem Persamaan Linear Dua Variabel (SPLDV)</a></p>
<p> </p>
<h3><span style="font-size: 14pt;">Cara Mencari Median</span></h3>
<p style="text-align: justify;">Seperti yang sudah disebutkan sebelumnya, untuk mencari nilai median, punya rumus yang berbeda. Setiap rumus ada perbedaannya, bergantung dari banyaknya data. Berikut <span style="font-weight: bold;">rumus mencari median</span> berdasarkan data ganjil dan data genap:</p>
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/d85f6c55-3d6e-4a1c-8678-78f85301b241.png" alt="rumus mencari median" width="600" height="400" /></p>
<p> </p>
<p style="text-align: justify;">Untuk data berjumlah ganjil, kamu bisa langsung ambil angka tengahnya. Tapi, untuk data berjumlah genap, akan ada 2 angka yang ditengah. Jadi, supaya kamu bisa peroleh nilai mediannya, harus pakai rumus yang berbeda. Nah, kalo kamu masih bingung dan nggak kebayang pakai rumusnya, mendingan kita langsung bahas soal yuk!</p>
<p> </p>
<h3><span style="font-size: 14pt;">Contoh Soal Mencari Median</span></h3>
<p style="text-align: justify;"><strong>Soal 1</strong></p>
<p style="text-align: justify;">Median dari data: 7, 8, 8, 9, 4, 3, 7, 9, 5, 7, 6, 5, 6 adalah …</p>
<p style="text-align: justify;"><span style="font-weight: bold;">Penyelesaian:</span></p>
<p style="text-align: justify;"><strong>Ingat ! urutkan nilainya dari terkecil sampai terbesar</strong></p>
<p style="text-align: justify;">3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9 <em>(n =13 termasuk data ganjil). </em>Maka, kamu bisa menggunakan rumus median untuk data ganjil, yaitu:</p>
<p style="text-align: justify;"><em><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-18-2021-12-42-01-56-PM.png" /></em></p>
<p>Sehingga, diperoleh nilai mediannya adalah 7.</p>
<p><strong>Soal 2</strong></p>
<p>Median dari data berikut adalah …<br />
<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-18-2021-12-42-51-85-PM.png" /></p>
<p><span style="font-weight: bold;">Penyelesaian:</span></p>
<p style="text-align: justify;">Kemudian, hitung dulu banyaknya data yang ada. Karena datanya genap, maka kamu bisa menggunakan rumus median untuk data genap, yaitu:</p>
<p><img loading="lazy" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/4e817967-6d46-4e82-a5de-d773e230f188.png" alt="contoh soal mencari median" width="600" height="400" /></p>
<p> </p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-18-2021-12-45-20-37-PM.png" /></p>
<p>Jadi diperoleh nilai mediannya, yaitu 7.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Modus (Nilai yang Sering Muncul)</span></h2>
<p style="text-align: justify;">Nah, untuk macam ukuran pemusatan data yang ketiga ini, pasti udah nggak asing lagi, kan? Yap, <span style="font-weight: bold;">modus adalah nilai yang paling sering muncul</span>. Jadi, dalam kelompok data, jika ada angka yang paling banyak ada (paling sering muncul), itu lah yang dinamakan modus. Biasanya, modus dilambangkan dengan Mo.</p>
<p style="text-align: justify;">Kalau data yang kamu peroleh merupakan data tunggal berkelompok atau data yang dikelompokkan ke dalam tabel, maka kamu bisa langsung lihat datum atau nilai dengan frekuensi paling tinggi. Tapi, kalo data tunggal biasa, kamu bisa gunakan tabel turus/ tally. Biar kamu paham kita ke contoh soal ya!</p>
<p> </p>
<h3><span style="font-size: 14pt;">Contoh Soal Mencari Modus</span></h3>
<p style="text-align: justify;">Modus dari data berikut adalah:</p>
<p style="text-align: justify;">102, 108, 106, 107, 108<br />
105, 107, 105, 108, 106<br />
106, 106, 107, 102, 105<br />
105, 102, 106, 105, 106<br />
107, 106, 105, 106, 102<br />
105, 107, 107, 106, 105<br />
106, 106, 105, 107, 102</p>
<p style="font-weight: bold;">Penyelesaian:</p>
<p>Nah, karena data di atas merupakan data tunggal biasa, agar lebih mudah, buat dalam bentuk tabel turus seperti ini:</p>
<p><img loading="lazy" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/cefbc60e-32f8-4a4b-aa33-202542b4541f.png" alt="tabel turus - mean, median, modus" width="600" height="400" /></p>
<p> </p>
<p style="text-align: justify;">Kemudian, kalau kita lihat, data yang paling sering muncul adalah 106 karena nilai frekuensinya paling tinggi, yaitu 11. Jadi, modus dari data itu adalah 106.</p>
<p style="text-align: justify;">Nah, kita udah bahas 3 ukuran pemusatan data nih. Sesuai janji di awal, kita bakal bahas cara mencari nilai salah satu siswa jika diketahui rata-rata nilai kelasnya. Caranya itu mirip banget sama soal di bawah ini, jadi pahami ya!</p>
<p><img loading="lazy" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Imported%20sitepage%20images/7a139030-47b7-460b-aa57-b40b7478165f.png" alt="contoh soal mean - ukuran pemusatan data" width="600" height="600" /></p>
<p style="font-weight: bold;">Baca Juga: <a id="__hsNewLink" href="/blog/teorema-pythagoras" rel="noopener">Bagaimana Cara Menghitung Teorema Pythagoras?</a></p>
<p> </p>
<p style="text-align: justify;">Wah, seru banget kan bahasan materi <strong>mean, median, dan modus</strong> ini. Soal-soal ukuran pemusatan data ini tuh bervariasi banget. Selain harus paham konsep, kamu juga harus terbiasa hitung cepat dan tepat.</p>
<p style="text-align: justify;">Caranya gimana tuhh supaya bisa hitung cepat dan tepat? Kamu harus perbanyak latihan, nah makanya setelah baca artikel ini langsung aja asah pemahaman dan kemampuan hitung kamu di <a style="font-weight: bold;" href="https://www.ruangguru.com/belajar?shortlink=eaff0eb9&pid=blog" rel="noopener">ruangbelajar</a>. Soal-soalnya bagus banget dijadikan latihan dan bisa mempertajam pemahaman kamu. Selamat belajar!</p>
<p style="text-align: justify;"><strong><a class="rg-cta" style="text-align: center;" href="https://app.ruangguru.com/" target="_blank" rel="noopener"><img loading="lazy" decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/cta/557819d0-f83b-4df6-a254-1dd7aaa6ca04.jpeg" alt="Bimbel Ruangguru" width="820" height="200" /></a></strong></p>
<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: left;">Kurniawan, (2013) Mandiri Matematika Untuk Kelas SMP/MTs Kelas VIII. Jakarta: Erlangga.</p>
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<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
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<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
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</picture>
</a>
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</picture>
</a>
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</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>