Yuk, kenali istilah-istilah statistik data tunggal dalam matematika! Ada mean, median, modus, jangkauan, kuartil, simpangan rata-rata, dan lain sebagainya. Baca artikel Matematika kelas 12 ini, ya!
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Siapa yang suka dengan proses pengolahan data dan angka-angka? Atau ada yang sudah pernah melakukan proses pengolahan data sebelumnya? Nah, proses pengolahan data ini erat sekali kaitannya dengan statistika, lho! Kamu tentu sudah familiar dengan istilah statistika, kan?
Dalam statistika, ada berbagai istilah nih, teman-teman. Di antaranya terdapat istilah-istilah statistik data tunggal. Data tunggal itu yang kayak gimana, sih? Data tunggal itu adalah data yang disusun sendiri menurut nilai dan besarnya masing masing. Kayak gini nih, contohnya:
5, 4, 7, 4, 6, 3, 7, 8
Nah, pada statistik data tunggal, ada 9 istilah yang harus kalian pahami. Kesembilan istilah tersebut adalah mean (rataan hitung), modus, median, jangkauan, kuartil, simpangan kuartil, simpangan rata-rata, ragam, dan simpangan baku.
Wah, banyak juga ya…
Eits, tapi tenang! Pembahasan di artikel ini nggak akan bikin kamu pusing kaya gambar header di atas, kok. Kalau nggak percaya, yuk baca sampai selesai!
1. Mean (Rata-Rata)
Teman-teman, mean atau disebut juga sebagai rata-rata atau rataan hitung merupakan rata-rata nilai hasil hitung. Maksudnya adalah nilai rata-rata yang muncul apabila seluruh data dijumlahkan dan dibagi sama rata sesuai jumlah data yang ada.
Contohnya yaitu nilai rata-rata ulangan matematikamu selama semester 1 di kelas XII. Hayoo, nilai rata-ratanya bagus nggak, nih? Atau ada yang justru masih penasaran gimana cara menghitungnya? Buat yang masih belum tau, nih, ada rumus yang bisa kamu pakai untuk menghitung mean atau rata-rata. Lihat rumusnya di bawah, ya!
Berdasarkan rumus di atas, mean bisa dihitung dengan cara menjumlahkan semua data, lalu hasilnya dibagi dengan banyaknya data yang ada. Misalnya kamu memiliki 5 data yang terdiri atas angka-angka sebagai berikut:
6, 9, 3, 5, 2
Maka, mean atau rata-ratanya adalah:
Jadi, mean atau rata-ratanya adalah 5. Mudah, kan? Sekarang, kita lanjut ke modus, yuk!
2. Modus
Modus yang dimaksud di sini bukan modus kriminal atau modus ke gebetan ya, teman-teman! Modus dalam statistika adalah data yang paling sering muncul atau data yang memiliki frekuensi terbesar di antara data-data lainnya.
Nah, sekarang coba kamu tebak, ya. Kalau di antara data tunggal berikut:
6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 5
Modusnya yang mana, hayoo?
Yup, betul! Modusnya adalah 9, karena 9 merupakan data yang paling sering muncul, dengan frekuensi sebesar 5. Biasanya, siswa paling suka ngerjain contoh soal modus nih, soalnya nggak perlu pake rumus yang ribet hehehe…
3. Median
Kamu sudah tau apa artinya median? Median itu adalah nilai tengah. Kamu tahu nggak, sih, untuk menentukan median, ada 2 kasus yang harus diperhatikan. Kasus pertama adalah median untuk data ganjil dan kasus kedua adalah untuk data genap. Kenapa dibagi 2 kasus? Karena rumus yang dipakai untuk menghitungnya itu berbeda ya, guys! Hmm… seperti apa sih, rumusnya? Coba perhatikan gambar berikut, ya!
Hati-hati, jangan sampai tertukar antara rumus median untuk data ganjil dengan rumus median untuk data genap, ya! Teliti lagi supaya hasil pengolahan data statistikamu tidak salah.
Untuk median, contoh soalnya adalah sebagai berikut:
Median dari data tunggal 7, 6, 5, 3, 4, 2, 7, 6, 7 adalah…
Sebelum menghitung median, kita harus mengurutkan terlebih dahulu data yang ada, dari nilai terkecil hingga terbesar. Jika diurutkan, maka data akan menjadi seperti berikut:
2, 3, 4, 5, 6, 6, 7, 7, 7
Lalu, karena n data tersebut adalah ganjil, yaitu 9, maka kita menggunakan rumus median untuk n ganjil, ya! Jadinya seperti berikut ini:
Jadi, mediannya adalah data ke-5, yaitu 6. Hayoo, jawabanmu betul, nggak?
4. Jangkauan (Range)
Sesuai dengan namanya, jangkauan atau disebut juga range (rentang) adalah nilai data yang paling besar dan nilai data yang paling kecil. Jangkauan digunakan untuk menghitung selisih nilai tertinggi dan nilai terkecil dalam kelompok data tersebut. Oleh karena itu, rumus yang digunakan untuk menghitung jangkauan adalah
R = xmax – xmin
Contoh soal:
Hitunglah jangkauan dari data tunggal di bawah ini:
2, 3, 10, 8, 2, 3, 5, 6, 7, 3, 10, 8, 2, 3, 5, 6, 7
R = xmax – xmin
R = 10 – 2
R = 8
Data terbesar (Xmax) dari data tersebut adalah 10, sedangkan data terkecilnya (Xmin) adalah 2. Maka, jangkauan dari data tunggal tersebut adalah 10 – 2 yaitu 8. Paham sampai sini? Yuk, lanjut lagi!
Baca Juga: Kombinasi dan Binomial Newton dalam Aturan Pencacahan
—
Sebelum kita bahas istilah statistika yang lain, kalo masih ada poin-poin yang belum kamu mengerti, mending belajar sama ahlinya, deh. Belajar bareng kakak-kakak pengajar di Ruangguru Privat Matematika misalnya.
Belajar nggak cuma menyenangkan, tapi kamu juga bakal diajari konsepnya sampai paham! Para pengajar di Ruangguru Privat juga sudah terstandarisasi kualitasnya, loh. Kamu juga bisa pilih nih, mau diajarkan secara langsung (offline) atau daring (online). Fleksibel, kan? Untuk info lebih lanjut, cuss klik link berikut!
5. Kuartil
Kuartil atau Qi adalah nilai yang membagi sekumpulan data yang telah diurutkan (dari terkecil hingga terbesar) ke dalam 4 bagian sama besar. Wah, maksudnya apa ya? Ilustrasinya kurang lebih seperti ini nih, simak baik-baik ya!
Ada tiga macam kuartil yaitu kuartil bawah (Q1), kuartil tengah atau sama saja dengan median (Q2), serta kuartil atas (Q3). Untuk contohnya kamu bisa lihat setelah pembahasan simpangan kuartil berikut ini, ya!
6. Simpangan Kuartil
Ada kuartil, ada simpangan kuartil. Hmm.. kalau simpangan kuartil itu apa, ya? Nah, yang dimaksud dengan simpangan kuartil adalah jangkauan dari ketiga kuartil itu sendiri. Kamu bisa menghitung simpangan kuartil dengan rumus berikut:
Rumusnya yaitu setengah dari Q3 dikurangi Q1. Wah, kalau rumusnya pendek gini, biasanya gampang mengingatnya, nih!
Contoh soal:
Hitunglah simpangan kuartil dari data berikut:
7, 10, 12, 14, 15, 17, 19, 20, 23, 25, 35
Tentukan terlebih dahulu Q1, Q2, dan Q3 nya. Berdasarkan pengertiannya, kuartil membagi sekumpulan data yang telah diurutkan (dari terkecil hingga terbesar) ke dalam 4 bagian sama besar. Maka Q1, Q2, dan Q3 nya adalah sebagai berikut:
7, 10, 12, 14, 15, 17, 19, 20, 23, 25, 35
Q1 Q2 Q3
Maka, simpangan kuartilnya adalah sebagai berikut:
Q3 dari data tersebut adalah 23 dan Q1 nya adalah 12, maka simpangan kuartil dari data tunggal tersebut adalah 5,5.
7. Simpangan Rata-Rata
Selain simpangan kuartil, ada juga yang namanya simpangan rata-rata. Simpangan rata-rata adalah rata-rata dari selisih data dengan nilai rata-rata datanya. Bingung, ya? Coba perhatikan rumus simpangan rata-rata berikut ini deh, supaya kamu lebih ada gambaran.
Rumus simpangan rata-rata ini agak panjang, jadi pastikan kamu memperhatikan dengan baik, ya! Oh iya, hasil penghitungan dari simpangan rata-rata itu selalu positif. Jadi, kalau hasilnya negatif, kayaknya kamu salah menghitungnya deh. Hehehe..
Contoh soal:
Simpangan rata-rata data 9, 3, 7, 8, 4, 5, 4, 8 adalah…
Untuk menghitung simpangan rata-rata, kita perlu menghitung rata-rata atau meannya terlebih dahulu, yakni sebagai berikut:
Setelah itu, kita gunakan rumus simpangan rata-rata, yakni sebagai berikut:
Jadi, simpangan rata-rata data tersebut adalah 2. Begitulah cara mencari simpangan rata-rata ya, gengs!
8. Ragam
Ragam yang dimaksud dalam statistik bukan ragam makanan favorit atau ragam acara televisi favorit, ya. Hihihi.. Ragam dalam statistika merupakan rata-rata dari kuadrat selisih data dengan nilai rata-rata datanya. Sama halnya dengan simpangan rata-rata, rumus dari ragam juga agak panjang nih, jadi perhatikan baik-baik, ya!
Langsung kita coba kerjakan contoh soal, yuk! Misalnya kita memiliki data sebagai berikut:
6, 7, 8, 8, 10, 9
Sama halnya dengan simpangan rata-rata, kita perlu menghitung meannya terlebih dahulu, yakni sebagai berikut:
Maka, ragam dari data tersebut adalah:
Jadi, ragam dari data tersebut adalah 1,67. Gimana? Sudah mulai pusing? Eits, jangan pusing duluu! Tinggal satu istilah lagi, nih!
9. Simpangan Baku
Istilah statistik data tunggal yang terakhir adalah simpangan baku, atau yang biasa dikenal dengan istilah deviasi standar. Kamu pasti pernah mendengar istilah ini, kan? Nah, simpangan baku itu adalah akar dari ragam. Rumusnya seperti ini, ya!
Untuk simpangan baku, gampang banget nih, buat ngapalin rumusnya. Kamu tinggal kasih akar saja pada rumus ragam, lalu selesai, deh! Kita coba contoh soal yang sama dengan ragam tadi, ya! Data yang kita punya adalah:
6, 7, 8, 8, 10, 9
Maka, mean atau rata-ratanya adalah:
Lalu, kita hitung simpangan bakunya menggunakan rumus sebagai berikut:
Bisa dilihat kan, kalau rumus simpangan baku itu adalah akar dari ragam. Karena ragamnya adalah 1,67, maka simpangan bakunya adalah 1,29. Begitu, guys!
Nah, sekian pembahasan kita tentang istilah-istilah statistik data tunggal. Ada mean (rataan hitung), modus, median, jangkauan, kuartil, simpangan kuartil, simpangan rata-rata, ragam, dan simpangan baku. Hmm.. ternyata banyak juga, ya! Apalagi rumus-rumusnya duh, bikin pusing 🙁
Eits, tapi tenang aja! Kalau kamu ingin memelajari materi seperti ini dalam bentuk video animasi, yuk tonton lewat ruangbelajar!
Referensi:
Sharma S. N., Widiastuti N., Himawan C., dkk. (2017). Jelajah Matematika SMA Kelas XII Program Wajib. Jakarta: Yudisthira.
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<h1 class="content-title">
Istilah-Istilah Statistik Data Tunggal dalam Matematika | Matematika Kelas 12 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kenya-swawikanti" class="">Kenya Swawikanti</a> </p>
<p class="content-info"><span>January 23, 2026 • </span> <span>7 minutes read</span></p>
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<p><span style="background-color: transparent;"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/8d34abe9-92ac-4532-bc60-05a33e1b68e3.png" alt="istilah data tunggal dalam Matematika" width="820" /></span></p>
<blockquote>
<p style="text-align: center; font-size: 16px;"><em><span style="background-color: transparent;">Yuk, kenali istilah-istilah statistik data tunggal dalam matematika! Ada mean, median, modus, jangkauan, kuartil, simpangan rata-rata, dan lain sebagainya. Baca <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-12">artikel Matematika kelas 12</a></strong> ini, ya!</span></em></p>
<p style="text-align: center; font-size: 16px;"><em><span style="background-color: transparent;">—</span></em></p>
</blockquote>
<p> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Siapa yang suka dengan proses pengolahan data dan angka-angka? Atau ada yang sudah pernah melakukan proses pengolahan data sebelumnya? Nah, proses pengolahan data ini erat sekali kaitannya dengan <a href="https://www.ruangguru.com/blog/statistika-dan-diagram-penyajian-data" rel="noopener"><span style="font-weight: bold;">statistika</span></a>, lho! Kamu tentu sudah familiar dengan istilah statistika, kan?</span></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Dalam statistika, ada berbagai istilah nih, teman-teman. Di antaranya terdapat istilah-istilah statistik data tunggal. </span><span style="background-color: transparent;">Data tunggal itu yang kayak gimana, sih? Data tunggal itu adalah <span style="font-weight: bold;">data yang disusun sendiri menurut nilai dan besarnya masing masing</span>. Kayak gini nih, contohnya:</span></p>
<p style="text-align: center;"><span style="background-color: transparent;"><span style="font-size: 14pt;">5, 4, 7, 4, 6, 3, 7, 8</span></span></p>
<p> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Nah, pada statistik data tunggal, a</span><span style="background-color: transparent; font-size: 1rem;">da 9 istilah yang harus kalian pahami. Kesembilan istilah tersebut adalah <span style="font-weight: bold;">mean (rataan hitung)</span>, <span style="font-weight: bold;">modus</span></span><em style="background-color: transparent; font-size: 1rem;">,</em><span style="background-color: transparent; font-size: 1rem;"><span style="font-weight: bold;"> median</span>, <span style="font-weight: bold;">jangkauan</span>, <span style="font-weight: bold;">kuartil</span>, <span style="font-weight: bold;">simpangan kuartil</span>, <span style="font-weight: bold;">simpangan rata-rata</span>, <span style="font-weight: bold;">ragam</span>, dan <span style="font-weight: bold;">simpangan baku</span>.</span></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Wah, banyak juga ya…</span></p>
<p style="text-align: justify;"><span style="background-color: transparent;"><em>Eits</em>, tapi tenang! Pembahasan di artikel ini nggak akan bikin kamu pusing kaya gambar <em>header</em> di atas, kok. Kalau nggak percaya, yuk baca sampai selesai! </span></p>
<p> </p>
<h2><span style="font-size: 18pt;">1. Mean (Rata-Rata)</span></h2>
<p style="text-align: justify;">Teman-teman, mean atau disebut juga sebagai rata-rata atau rataan hitung merupakan <span style="font-weight: bold;">rata-rata nilai hasil hitung</span><span style="font-weight: normal;">.</span> Maksudnya adalah nilai rata-rata yang muncul apabila seluruh data dijumlahkan dan dibagi sama rata sesuai jumlah data yang ada.</p>
<p style="text-align: justify;">Contohnya yaitu <span style="font-weight: normal;">nilai rata-rata ulangan matematikamu selama semester 1 di kelas XII</span>. <em>Hayoo</em>, nilai rata-ratanya bagus nggak, nih? Atau ada yang justru masih penasaran gimana cara menghitungnya? Buat yang masih belum tau, nih, ada rumus yang bisa kamu pakai untuk menghitung mean atau rata-rata. Lihat rumusnya di bawah, ya!</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20mean.jpg" alt="rumus mean" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Berdasarkan rumus di atas, mean bisa dihitung dengan cara <span style="font-weight: bold;">menjumlahkan semua data, lalu hasilnya dibagi dengan banyaknya data yang ada</span>. Misalnya kamu memiliki 5 data yang terdiri atas angka-angka sebagai berikut:</p>
<p style="text-align: center;"><span style="font-size: 14pt;">6, 9, 3, 5, 2</span></p>
<p> </p>
<p style="text-align: justify;">Maka, <span style="font-weight: normal;">mean atau rata-ratanya</span> adalah:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 199px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20mean.png" alt="contoh soal mean" width="199" /></p>
<p style="text-align: justify;">Jadi, <span style="font-weight: bold;">mean</span> <span style="font-weight: bold;">atau rata-ratanya</span> <span style="font-weight: bold;">adalah 5</span>. Mudah, kan? Sekarang, kita lanjut ke modus, yuk!</p>
<p> </p>
<h2><span style="font-size: 18pt;">2. Modus</span></h2>
<p style="text-align: justify;">Modus yang dimaksud di sini bukan modus kriminal atau modus ke gebetan ya, teman-teman! Modus dalam statistika adalah <span style="font-weight: bold;">data yang paling sering muncul</span> <span style="font-weight: normal;">atau </span><span style="font-weight: bold;">data yang memiliki frekuensi terbesar</span> di antara data-data lainnya.</p>
<p style="text-align: justify;">Nah, sekarang coba kamu tebak, ya. Kalau di antara data tunggal berikut:</p>
<p style="text-align: center;"><span style="font-size: 14pt;">6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 5</span></p>
<p> </p>
<p style="text-align: justify;">Modusnya yang mana, <em>hayoo</em>?</p>
<p style="text-align: justify;">Yup, betul! <span style="font-weight: bold;">Modusnya adalah</span> <span style="font-weight: bold;">9</span>, karena 9 merupakan data yang paling sering muncul, dengan frekuensi sebesar 5. Biasanya, siswa paling suka ngerjain contoh soal modus nih, soalnya nggak perlu pake rumus yang ribet <em>hehehe</em>…</p>
<p> </p>
<h2><span style="font-size: 18pt;">3. Median</span></h2>
<p style="text-align: justify;">Kamu sudah tau apa artinya median? Median itu adalah <span style="font-weight: bold;">nilai tengah</span>. Kamu tahu nggak, sih, untuk menentukan median, ada <span style="font-weight: bold;">2 kasus yang harus diperhatikan</span>. Kasus pertama adalah <span style="font-weight: normal;">median untuk</span><span style="font-weight: bold;"> data ganjil</span> dan kasus kedua adalah <span style="font-weight: normal;">untuk</span><span style="font-weight: bold;"> data genap</span>. Kenapa dibagi 2 kasus? Karena rumus yang dipakai untuk menghitungnya itu berbeda ya, <em>guys</em>! <em>Hmm</em>… seperti apa sih, rumusnya? Coba perhatikan gambar berikut, ya!</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20median%20n%20ganjil%20dan%20n%20genap.jpg" alt="rumus median n ganjil dan n genap" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Hati-hati, jangan sampai tertukar antara rumus median untuk data ganjil dengan rumus median untuk data genap, ya! Teliti lagi supaya hasil pengolahan data statistikamu tidak salah.</p>
<p style="text-align: justify;">Untuk median, contoh soalnya adalah sebagai berikut:</p>
<p style="text-align: justify;">Median dari data tunggal <span style="font-weight: bold;">7, 6, 5, 3, 4, 2, 7, 6, 7</span> adalah…</p>
<p style="text-align: justify;">Sebelum menghitung median, kita harus <span style="font-weight: bold;">mengurutkan</span> terlebih dahulu data yang ada, <span style="font-weight: bold;">dari nilai terkecil hingga terbesar</span>. Jika diurutkan, maka data akan menjadi seperti berikut:</p>
<p style="text-align: center;"><span style="font-size: 14pt;">2, 3, 4, 5, 6, 6, 7, 7, 7</span></p>
<p> </p>
<p style="text-align: justify;">Lalu, karena n data tersebut adalah <span style="font-weight: bold;">ganjil</span>, yaitu 9, maka kita menggunakan <span style="font-weight: bold;">rumus median untuk n ganjil</span>, ya! Jadinya seperti berikut ini:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 156px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20median.png" alt="contoh soal median" width="156" /></p>
<p style="text-align: justify;">Jadi, <span style="font-weight: bold;">mediannya adalah data ke-5, yaitu 6</span>. <em>Hayoo</em>, jawabanmu betul, nggak?</p>
<p> </p>
<h2><span style="font-size: 18pt;">4. Jangkauan (<em>Range</em>)</span></h2>
<p style="text-align: justify;">Sesuai dengan namanya, <span style="font-weight: normal;">jangkauan atau disebut juga <em>range</em> (rentang) adalah nilai data yang paling besar dan nilai data yang paling kecil</span>. Jangkauan digunakan untuk <span style="font-weight: bold;">menghitung selisih nilai tertinggi dan nilai terkecil</span> dalam kelompok data tersebut. Oleh karena itu, rumus yang digunakan untuk menghitung jangkauan adalah</p>
<p style="text-align: center;"><span style="font-size: 14pt;"><strong>R = x<sub>max </sub>– x<sub>min</sub></strong></span></p>
<p> </p>
<p style="text-align: justify;"><span style="font-weight: normal;">Contoh soal:</span></p>
<p style="text-align: justify;"><span style="font-weight: normal;">Hitunglah jangkauan dari data tunggal di bawah ini:</span></p>
<p style="text-align: center;"><span style="font-size: 14pt;">2, 3, 10, 8, 2, 3, 5, 6, 7, 3, 10, 8, 2, 3, 5, 6, 7</span></p>
<p> </p>
<p style="text-align: justify; font-weight: normal;">R = x<sub>max </sub>– x<sub>min</sub></p>
<p style="text-align: justify;">R = 10 – 2</p>
<p style="text-align: justify;">R = 8</p>
<p style="text-align: justify;"><span style="font-weight: bold;">Data terbesar (X<sub>max</sub>)</span> dari data tersebut adalah <span style="font-weight: bold;">10</span>, sedangkan <span style="font-weight: bold;">data terkecilnya (X<sub>min</sub>)</span> adalah <span style="font-weight: bold;">2</span>. Maka, <span style="font-weight: bold;">jangkauan</span> dari data tunggal tersebut <span style="font-weight: bold;">adalah 10 – 2 yaitu</span> <span style="font-weight: bold;">8</span>. <span style="font-weight: normal;">Paham sampai sini? Yuk, lanjut lagi!</span></p>
<p style="font-weight: bold;">Baca Juga: <a href="https://www.ruangguru.com/blog/kombinasi-dan-binomial-newton">Kombinasi dan Binomial Newton dalam Aturan Pencacahan</a></p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Sebelum kita bahas istilah statistika yang lain, kalo masih ada poin-poin yang belum kamu mengerti, mending belajar sama ahlinya, deh. Belajar bareng kakak-kakak pengajar di <a href="https://www.ruangguru.com/privat/matematika"><strong>Ruangguru Privat Matematika</strong></a> misalnya.</p>
<p style="text-align: justify;">Belajar nggak cuma menyenangkan, tapi kamu juga bakal diajari konsepnya sampai paham! Para pengajar di Ruangguru Privat juga sudah terstandarisasi kualitasnya, loh. Kamu juga bisa pilih nih, mau diajarkan secara langsung (<em>offline</em>) atau daring (<em>online</em>). Fleksibel, kan? Untuk info lebih lanjut, cuss klik link berikut!</p>
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<p> </p>
<h2><span style="font-size: 18pt;">5. Kuartil</span></h2>
<p style="text-align: justify;">Kuartil atau Q<sub>i</sub> adalah nilai yang <span style="font-weight: bold;">membagi sekumpulan data yang telah diurutkan (dari terkecil hingga terbesar) ke dalam 4 bagian sama besar</span>. Wah, maksudnya apa ya? Ilustrasinya kurang lebih seperti ini nih, simak baik-baik ya!</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/kuartil.jpg" alt="kuartil" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Ada tiga macam kuartil yaitu <span style="font-weight: bold;">kuartil bawah (Q<sub>1</sub>)</span>, <span style="font-weight: bold;">kuartil tengah</span> atau sama saja dengan <span style="font-weight: bold;">median (Q<sub>2</sub>)</span>, serta <span style="font-weight: bold;">kuartil atas (Q<sub>3</sub>)</span>. Untuk contohnya kamu bisa lihat setelah pembahasan simpangan kuartil berikut ini, ya!</p>
<p> </p>
<h2><span style="font-size: 18pt;">6. Simpangan Kuartil</span></h2>
<p style="text-align: justify;">Ada kuartil, ada simpangan kuartil. <em>Hmm</em>.. kalau simpangan kuartil itu apa, ya? Nah, yang dimaksud dengan simpangan kuartil adalah <span style="font-weight: bold;">jangkauan dari ketiga kuartil itu sendiri</span>. Kamu bisa menghitung simpangan kuartil dengan rumus berikut:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20simpangan%20kuartil.jpg" alt="rumus simpangan kuartil" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Rumusnya yaitu setengah dari Q<sub>3</sub> dikurangi Q<sub>1</sub>. Wah, kalau rumusnya pendek gini, biasanya gampang mengingatnya, nih!</p>
<p style="text-align: justify;">Contoh soal:</p>
<p style="text-align: justify;">Hitunglah simpangan kuartil dari data berikut:</p>
<p style="text-align: center;"><span style="font-size: 14pt;">7, 10, 12, 14, 15, 17, 19, 20, 23, 25, 35</span></p>
<p> </p>
<p style="text-align: justify;">Tentukan terlebih dahulu Q<sub>1</sub>, Q<sub>2</sub>, dan Q<sub>3</sub> nya. Berdasarkan pengertiannya, kuartil membagi sekumpulan data yang telah diurutkan (dari terkecil hingga terbesar) ke dalam 4 bagian sama besar. Maka Q<sub>1</sub>, Q<sub>2</sub>, dan Q<sub>3</sub> nya adalah sebagai berikut:</p>
<p style="text-align: justify;">7, 10, <span style="font-weight: bold;">12</span>, 14, 15, <span style="font-weight: bold;">17</span>, 19, 20, <span style="font-weight: bold;">23</span>, 25, 35</p>
<p style="text-align: justify;"> <span style="font-weight: bold;">Q<sub>1</sub></span> <span style="font-weight: bold;">Q<sub>2</sub></span><span style="font-weight: normal;"> </span><span style="font-weight: bold;">Q<sub>3</sub></span></p>
<p> </p>
<p style="text-align: justify;">Maka, simpangan kuartilnya adalah sebagai berikut:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 226px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20simpangan%20kuartil.png" alt="contoh soal simpangan kuartil" width="226" /></p>
<p style="text-align: justify;"><span style="font-weight: bold;">Q<sub>3</sub></span> dari data tersebut <span style="font-weight: normal;">adalah </span><span style="font-weight: bold;">23</span> dan <span style="font-weight: bold;">Q<sub>1</sub></span> nya <span style="font-weight: normal;">adalah </span><span style="font-weight: bold;">12</span>, maka <span style="font-weight: bold;">simpangan kuartil</span> dari data tunggal tersebut <span style="font-weight: bold;">adalah 5,5</span>.</p>
<p> </p>
<h2><span style="font-size: 18pt;">7. Simpangan Rata-Rata</span></h2>
<p style="text-align: justify;">Selain simpangan kuartil, ada juga yang namanya simpangan rata-rata. Simpangan rata-rata adalah <span style="font-weight: bold;">rata-rata dari selisih data dengan nilai rata-rata datanya</span>. Bingung, ya? Coba perhatikan rumus simpangan rata-rata berikut ini deh, supaya kamu lebih ada gambaran.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20simpangan%20rata-rata.jpg" alt="rumus simpangan rata-rata" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Rumus simpangan rata-rata ini agak panjang, jadi pastikan kamu memperhatikan dengan baik, ya! Oh iya, hasil penghitungan dari simpangan rata-rata itu <span style="font-weight: bold;">selalu positif</span>. Jadi, kalau hasilnya negatif, kayaknya kamu salah menghitungnya deh. <em>Hehehe</em>..</p>
<p style="text-align: justify;">Contoh soal:</p>
<p style="text-align: justify;">Simpangan rata-rata data <span style="font-weight: bold;">9, 3, 7, 8, 4, 5, 4, 8</span> adalah…</p>
<p style="text-align: justify;">Untuk menghitung simpangan rata-rata, kita perlu menghitung <span style="font-weight: bold;">rata-rata atau meannya</span> terlebih dahulu, yakni sebagai berikut:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 296px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20simpangan%20rata-rata%201.png" alt="contoh soal simpangan rata-rata 1" width="296" /></p>
<p style="text-align: justify;">Setelah itu, kita gunakan rumus <span style="font-weight: bold;">simpangan rata-rata</span>, yakni sebagai berikut:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 621px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20simpangan%20rata-rata%202.png" alt="contoh soal simpangan rata-rata 2" width="621" /></p>
<p style="text-align: justify;">Jadi, <span style="font-weight: bold;">simpangan rata-rata</span> <span style="font-weight: bold;">data tersebut</span> <span style="font-weight: bold;">adalah 2</span>. Begitulah cara mencari simpangan rata-rata ya, <em>gengs</em>!</p>
<p> </p>
<h2><span style="font-size: 18pt;">8. Ragam</span></h2>
<p style="text-align: justify;">Ragam yang dimaksud dalam statistik bukan ragam makanan favorit atau ragam acara televisi favorit, ya. <em>Hihihi</em>.. Ragam dalam statistika merupakan <span style="font-weight: bold;">rata-rata dari kuadrat selisih data dengan nilai rata-rata datanya</span><span style="font-weight: normal;">. Sama halnya dengan simpangan rata-rata, </span>rumus dari ragam juga agak panjang nih, jadi perhatikan baik-baik, ya!</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20ragam.jpg" alt="rumus ragam" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Langsung kita coba kerjakan contoh soal, yuk! Misalnya kita memiliki data sebagai berikut:</p>
<p style="text-align: center;"><span style="font-size: 14pt;">6, 7, 8, 8, 10, 9</span></p>
<p> </p>
<p style="text-align: justify;">Sama halnya dengan simpangan rata-rata, kita perlu menghitung <span style="font-weight: bold;">meannya</span> terlebih dahulu, yakni sebagai berikut:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 254px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20ragam%201.png" alt="contoh soal ragam 1" width="254" /></p>
<p style="text-align: justify;">Maka, <span style="font-weight: bold;">ragam</span> dari data tersebut adalah:</p>
<p><img decoding="async" style="width: 631px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20ragam%202.png" alt="contoh soal ragam 2" width="631" /></p>
<p style="text-align: justify;">Jadi, <span style="font-weight: bold;">ragam dari data tersebut adalah</span> <span style="font-weight: bold;">1,67</span>. Gimana? Sudah mulai pusing? <em>Eits</em>, jangan pusing duluu! Tinggal satu istilah lagi, nih!</p>
<p> </p>
<h2><span style="font-size: 18pt;">9. Simpangan Baku</span></h2>
<p style="text-align: justify;">Istilah statistik data tunggal yang terakhir adalah simpangan baku, atau yang biasa dikenal dengan istilah <span style="font-weight: bold;">deviasi standar</span>. Kamu pasti pernah mendengar istilah ini, kan? Nah, simpangan baku itu adalah <span style="font-weight: bold;">akar dari ragam</span>. Rumusnya seperti ini, ya!</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20simpangan%20baku.jpg" alt="rumus simpangan baku" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Untuk simpangan baku, gampang banget nih, buat ngapalin rumusnya. Kamu tinggal kasih akar saja pada rumus ragam, lalu selesai, deh! Kita coba <span style="font-weight: bold;">contoh soal yang sama dengan ragam tadi</span>, ya! Data yang kita punya adalah:</p>
<p style="text-align: center;"><span style="font-size: 14pt;">6, 7, 8, 8, 10, 9</span></p>
<p> </p>
<p style="text-align: justify;">Maka, <span style="font-weight: bold;">mean atau rata-ratanya</span> adalah:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 254px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20ragam%201.png" alt="contoh soal ragam 1" width="254" /></p>
<p style="text-align: justify;">Lalu, kita hitung <span style="font-weight: bold;">simpangan bakunya</span> menggunakan rumus sebagai berikut:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 680px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20simpangan%20baku.png" alt="contoh soal simpangan baku" width="680" /></p>
<p style="text-align: justify;">Bisa dilihat kan, kalau rumus simpangan baku itu adalah <span style="font-weight: bold;">akar dari ragam</span>. Karena <span style="font-weight: bold;">ragamnya adalah</span> <span style="font-weight: bold;">1,67</span>, maka <span style="font-weight: bold;">simpangan bakunya adalah</span> <span style="font-weight: bold;">1,29</span>. Begitu, <em>guys</em>!</p>
<p style="text-align: justify;">Nah, sekian pembahasan kita tentang istilah-istilah statistik data tunggal. Ada <span style="font-weight: bold;">mean (rataan hitung), modus, median, jangkauan, kuartil, simpangan kuartil, simpangan rata-rata, ragam, </span><span style="font-weight: normal;">dan </span><span style="font-weight: bold;">simpangan baku</span>. <em>Hmm</em>.. ternyata banyak juga, ya! Apalagi rumus-rumusnya duh, bikin pusing 🙁</p>
<p style="text-align: justify;"><em>Eits</em>, tapi tenang aja! Kalau kamu ingin memelajari materi seperti ini dalam bentuk video animasi, yuk tonton lewat <strong><a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener">ruangbelajar!</a></strong></p>
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<p><strong>Referensi: </strong></p>
<p>Sharma S. N., Widiastuti N., Himawan C., dkk. (2017). <em>Jelajah Matematika SMA Kelas XII Program Wajib</em>. Jakarta: Yudisthira.</p>
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// 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">
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<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
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<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>