WEBVTT

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Selamat datang ke dunia Statistik.

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Sesuatu yg dah lama saya nantikan.

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Saya akan terus saja kpd isi penting

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dan akan mencuba sebanyak mungkin cth latihan

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supaya anda lebih faham tentang Statistik.

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Sebagai permulaan utk yg belum arif

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walaupun saya rasa ramai yg sudah

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tahu tentang Statistik.

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Secara umum,

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Statistik berkait dgn data.

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Statistik boleh di bahagi kpd

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3 bahagian iaitu:

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Diskriptif:

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Cth: anda ada sekumpulan data

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yg hanya diberi sebahagian saja kpd orang lain.

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Mungkin anda lebih suka mewakili data itu

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dgn nombor atau simbol, tanpa

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mendedahkan butirannya.

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Itu cth bagi Diskriptif.

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Ada juga bersifat Ramalan.

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Jadi cabang ke-2 ialah

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Inferensi:

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Kaedah utk merumuskan sesuatu

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menggunakan data.

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Cth: bila anda ambil sampel data dari 
suatu populasi.

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*kita akan guna banyak cth sampel 
melawan populasi

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*yg mana anda mungkin sudah biasa guna.

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Katakan kajian tentang 3 org yg

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akan mengundi utk Presiden.
Jelas sekali, kajian bukan pd populasi

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tapi kpd sampel

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Statistik Inferensi bermaksud

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inferens atau kesimpulan kpd populasi

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boleh dibuat melalui 
pengiraan terhadap sampel.

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Itulah gambaran kasar tentang Statistik.

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Kita akan mulakan cth latihan

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tentang Statistik: Diskriptif

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Mula-mula,

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berikan 1 nilai yg mewakili

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seluruh nombor dlm suatu set nombor.

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Nilai itu dipanggil Kecenderungan Memusat.

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Istilah ini banyak diguna dlm buku Statistik.

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Kecenderungan Memusat,

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juga disebut sbg Purata atau nilai tengah.

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Ada pelbagai cara utk mengira

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Purata sesuatu set nombor.

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Anda mungkin biasa dgn kaedah ini:

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Mean,

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Median (med), dan Mod.

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Dlm Statistik, 3 kaedah ini

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mewakili Purata bagi data dlm populasi

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atau data dlm sampel.

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Kesemua nilai bg kaedah ini

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adalah dlm bentuk Purata.

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Kita akan buat latihan utk

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lebih kefahaman.

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Biasanya, Purata yg kita guna pakai

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seharian itu ialah Mean.

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Bukan Purata dlm bentuk Median atau Mod.

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Katakan ada no. 1,

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dan 1 lagi,
2, 3,

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dan 4.

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Asas Purata:
jumlahkan kesemua nombor

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÷ bilangan nombor.

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Jadi, 
1 + 1 + 2 + 3 + 4

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dan ÷ dgn 5 bilangan nombor.

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(1 + 1 + 2 + 3 + 4) ÷ 5 = 11/5

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11/5 = 2.2

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Maka, 2.2 ialah Kecenderungan Memusat kpd

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set nombor ini.

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Atau, ringkasnya ialah Purata.

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Bahasa yg lebih tepat dlm Statistik

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ialah Mean Aritmetik.

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Selesai utk kaedah Mean.

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Cara lain ialah

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dgn menyusun semula nombor mengikut urutan.

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Kita susun semula set nombor ini.

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1, 1, 2, 3, 4.

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Ambil nombor yg tengah.

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Ada 5 nombor semuanya.

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Maka ini ialah nombor yg tengah, kan?

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Nombornya ialah 2.

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Ada 2 no. yg > dari 2,

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dan 2 no. yg < dari 2.

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Cara ini dipanggil Median (Med).

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Di mana kita susun semula set nombor,

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dan cari no. yg mana

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nilai lebih besar/kecil nya 
adalah sama banyak.

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Maka Med bg set ini ialah 2.

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Perhatikan, nilainya hampir dgn Mean.

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Ingat, tiada jawapan tepat yg dicari.

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Tak perlu membandingkan jawapan.

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Kita cuma belajar tentang kaedah yg berbeza
utk mencari Purata.

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Cara ini mudah dgn cuma 5 no. saja.

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Bagaimana jika ada 6 no. atau lebih?

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Katakan set no kita ialah

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1, 1, 2, 3, 4, 4

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Tiada no di tengah, kan?

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2 bukan lagi no. tengah sebab
ada 2 no. <

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dan 3 no. > dari nya.

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3 juga bukan no. tengah sebab
ada 3 no. <

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dan 2 no. > .

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Jadi sekarang tiada nilai tengah.

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Maka, cara utk dapatkan Med

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bg set no. dgn bilangan genap ialah:

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cari Purata bg 2 no. tengah dlm set.

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Dlm kes ini, Med = (2+3) ÷ 2 = 2.5

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Perhatikan Mean & Med set no. ini.

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Sekarang kita cuba kaedah Mod pula.

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Mod ialah cara termudah 
utk mencari Kecenderungan Memusat

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atau Purata sesuatu set.

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Asasnya, Mod ialah kekerapan sesuatu no. dlm set.

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Dari set ini, ada 2 no.1,

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dan 1 saja kekerapan no.lain

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Maka, Mod set ini ialah 1.

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Bagaimana pula dgn cth set ini?

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1, 1, 2, 3, 4, 4
Ada 2 x no.1 & no.4

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Set ini sedikit mencabar

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kerana jawapannya agak samar.

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Tapi biasanya dlm ujian,


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jawapan yg dicari ialah no. yg tepat.

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Pasti ada Mod yg tepat dlm sesuatu set.

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Anda mungkin tertanya-tanya

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kenapa tak guna kaedah Purata 
yg biasa saja?

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Atau cuma guna kaedah Mean saja?

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Apa fungsi Median & Mod?

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Kita buat beberapa lg cth latihan utk

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mendapat lebih kefahaman.

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Katakan kita ada set no berikut:

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3, 3, 3, 3, 3, 100

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Apakah Mean Aritmetik bagi set ini?

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Ada 5 x no.3 dan 1 saja no.100

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Jadi, 
Mean = 115 ÷ 6

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Mean = 115 ÷ 6 = 19 1/6

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Jumlahkan saja kesemua nombor dan 


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÷ dgn bilangan no. dlm set.

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Tapi adakah nilai ini

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benar mewakili set tersebut?

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Anda mungkin rasa Kecenderungan Memusat, 
atau Purata set ini

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bernilai hampir dgn 3. 
Sebab no.3 berulang, kan?

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Apa kata kita cari Med pula?

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No. dlm set ini sedia tersusun, kan?

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Maka yg mana kah nilai tengah nya?

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Bg set no. dgn bilangan genap, 
ambil 2 no. yg tengah

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iaitu no. 3 & 3

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Puratakan 3 & 3,

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atau

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kirakan Mean bg (3 + 3) ÷ 2 = 3

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Mungkin cara ini lebih sesuai utk mengira

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Kecenderungan Memusat atau Purata 
set no ini, kan?

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Dgn pengiraan secara Med,

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no. dgn nilai > tak berbeza fungsi

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dgn nilai yg <.

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Dlm Statistik, 
istilahnya Titik Terpencil (Outlier)

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Dlm cth harian, purata harga rumah

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dlm sesebuah bandar bernilai $100k.

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Ada juga yg bernilai $1trillion.

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Sekiranya anda diberitahu yg purata 


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harganya ialah $1j, 
kemungkinan anda telah dapat

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maklumat yg tidak tepat.

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Tapi, katakan harga Med bg sesebuah rumah 
ialah $100k,

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itu lebih logik kpd pembeli.

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Sama kes dgn latihan ini.

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Median memberi anda gambaran tentang 
keseluruhan set no. ini

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Titik Terpencil (Outlier) bermaksud

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satu no. yg menonjol atau jauh berbeza

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dgn no. lain, cth nya ukuran.

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Akhir sekali, cth tentang Mod.

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Dari set ini, apakah Mod yg dikenalpasti?

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ada 5 x no.3 dan 1 x no.100.

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Maka jelas, Mod = 3.

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Kesimpulannya, Titik Terpencil,
Median, dan Mod

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memberikan anda gambaran tentang 


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keadaan sesebuah populasi itu.

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Cthnya: Ia boleh membuktikan

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ada kesilapan dlm 
sesuatu ukuran.

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Atau cth bg harga rumah. 


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Kita boleh mengetahui perbezaan jelas h

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arga-harga rumah di sesebuah kawasan.

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Katakan utk cth markah ujian,

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jelas di situ 1 dari 6 org pelajar 


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yg sangat cemerlang 
berbanding kawan-kawannya.

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Maka, ini menunjukkan tahap pembelajaran

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bagi pelajar kelas itu.

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Selesai sudah dgn cth latihan.

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Saya cadangkan anda cuba dgn nilai

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dan konsep yg berkaitan.

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Kita akan belajar lebih tentang
Statistik: Diskriptif dlm video lain.

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Kita akan bincang topik lain

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selain Kecenderungan Memusat.

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Jumpa lagi dlm video yg lain!