Isilinganiso: Isilinganiso noma Isilinganiso
Isilinganiso, noma isilinganiso, singenye yemiqondo eyisisekelo kakhulu kwizibalo. Sivame ukusetshenziswa emikhakheni ehlukahlukene, kusukela kwezemfundo nakwezomnotho kuya kwisayensi. Kulesi sihloko, sizoxoxa ngokujulile ngokuthi isilinganiso siyini, ukuthi singabalwa kanjani, nokuthi sihunyushwa futhi sisetshenziswa kanjani ekuphileni kwansuku zonke.
Kuyini i-Mean?
Isilinganiso yinani elitholakala ngokuhlukanisa inani eliphelele lesethi yedatha ngenani lamaphuzu edatha. Kumathematika, isilinganiso sivame ukuchazwa ngokuthi "isilinganiso sezibalo." Leli gama livela kwelesiLatini elithi "medius," elisho "phakathi." Isibonelo, uma othile ethi inani elimaphakathi lesethi yedatha lingu-10, kusho ukuthi uma wonke amaphuzu edatha ehlukaniswe ngokulinganayo, iphuzu ngalinye ledatha lizoba nenani elingu-10.
Ngokwezibalo, isilinganiso singabhalwa ngale ndlela elula elandelayo:
\[ \text{Mean} = \frac{\sum x_i}{N} \]
Di mana:
– \( \sum x_i \) yisamba sawo wonke amanani kusethi yedatha.
– \( N \) inani eliphelele ledatha.
Indlela Yokubala Isilinganiso
Ake sibheke isibonelo ukuze siqonde ukuthi singabala kanjani isilinganiso ngokucacile. Ake sithi sinesethi yedatha elandelayo: [4, 8, 15, 16, 23, 42].
1. Hlanganisa yonke idatha:
\[
4 + 8 + 15 + 16 + 23 + 42 = 108
\]
2. Bala inani ledatha:
\[
N = 6
\]
3. Bala isilinganiso:
\[
\text{Mean} = \frac{108}{6} = 18
\]
Ngakho-ke, isilinganiso sedatha singu-18.
Isilinganiso Ezimweni Ezihlukahlukene
I-mean isetshenziswa ezimweni ezahlukene futhi inezinhlelo zokusebenza eziningi:
1. Imfundo: Izindlela zivame ukusetshenziswa ukubala amaphuzu okuhlolwa ajwayelekile abafundi ekilasini. Lokhu kusiza othisha ukuthi banqume ukuthi ikilasi lisebenza kahle kangakanani lilonke.
2. Ezomnotho: Kwezomnotho, isilinganiso sivame ukusetshenziswa ukubala isilinganiso semali engenayo, izindleko, amanani, njll. Isibonelo, isilinganiso semali engenayo yezwe ngomuntu ngamunye singanikeza umbono jikelele wenhlalakahle yezomnotho yezwe.
3. Isayensi: Emikhakheni eyahlukene yesayensi, isilinganiso sisetshenziswa ukucubungula nokuhlaziya idatha yokuhlola. Isibonelo, ocwaningweni lwezokwelapha, isilinganiso sisetshenziswa ukunquma ukusebenza kahle komuthi ngokubala umphumela wokwelashwa ojwayelekile ezigulini.
Isilinganiso, Isilinganiso, kanye Nemodi
Isilinganiso sivame ukuqhathaniswa nezinye izinhlobo ezimbili zezilinganiso: i-median kanye ne-mode. Nakuba zonke ezintathu ziyizilinganiso zokuthambekela okuphakathi, zinomehluko oyisisekelo:
1. I-Median: I-Median yinani eliphakathi ohlwini oluhleliwe lwedatha. Uma inani ledatha lingalingani, i-Median yinani eliphakathi. Uma inani ledatha lilingana, i-Median iyisilinganiso samanani amabili aphakathi.
2. Imodi: Imodi yinani elivela kaningi kudatha. Isethi yedatha ingaba nemodi eyodwa, ezingaphezu kweyodwa, noma ngisho ingabi nayo nhlobo.
Isethi yedatha yesibonelo: [4, 8, 15, 16, 23, 42]
– Isilinganiso: 18
– Okuphakathi: (15 + 16) / 2 = 15.5
– Imodi: Akukho ngoba inani ngalinye livela kanye kuphela.
Izinzuzo kanye nokungalungi kwe-Mean
Izinzuzo:
1. Kulula Ukubala: Isilinganiso kulula kakhulu ukubala nokuyiqonda, ngokumane uhlanganise yonke idatha bese uyihlukanisa ngenani ledatha.
2. Ukusebenzisa Yonke Idatha: Isilinganiso sicabangela yonke idatha esethini yedatha, ngaleyo ndlela sinikeze ukumelwa okuphelele.
Ukushoda:
1. Kuyazwela Kumanani Aphezulu: Isilinganiso singathonywa kakhulu amanani aphezulu noma izinto ezingaphandle, ngakho-ke kungenzeka ukuthi asimeli idatha ngokunembile ngaso sonke isikhathi.
2. Ayinikezi Ulwazi Ngokusatshalaliswa Kwedatha: Isilinganiso sinikeza isilinganiso kuphela, ngaphandle kolwazi mayelana nokuthi idatha isatshalaliswa kanjani kuleyo silinganiso.
Ukusetshenziswa kwe-Mean ekuHlaziyweni kwedatha
Ucwaningo Lwecala: Amabanga Abafundi
Ake sithi sifuna ukuhlaziya amaphuzu okuhlolwa kwezibalo abafundi abayi-10: [55, 60, 61, 62, 65, 68, 70, 75, 85, 90].
1. Bala isilinganiso:
\[
\text{Mean} = \frac{55 + 60 + 61 + 62 + 65 + 68 + 70 + 75 + 85 + 90}{10} = 69.1
\]
2. Incazelo:
Amaphuzu aphakathi kwabafundi abayi-10 ayengu-69.1. Lokhu kusho ukuthi, ngokwesilinganiso, amaphuzu abafundi abawathola ezivivinyweni zezibalo ayengu-69.1.
Umphumela Wezindinganiso Eziphakeme:
Ake sithi umfundi oyedwa othole amaphuzu angu-55 ekuqaleni akazange abhale isivivinyo futhi wanikwa amaphuzu angu-0. Isethi yedatha entsha: [0, 60, 61, 62, 65, 68, 70, 75, 85, 90].
1. Bala isilinganiso ngamanani aphakeme kakhulu:
\[
\text{Mean} = \frac{0 + 60 + 61 + 62 + 65 + 68 + 70 + 75 + 85 + 90}{10} = 63.6
\]
2. Incazelo:
Ngenani elilodwa elidlulele elingu-0, isilinganiso sehla siye ku-63.6. Lokhu kubonisa ukuthi isilinganiso sibucayi kangakanani kumanani adlulele.
Ukunciphisa Ukuzwela Kumanani Aphezulu
Ezinye izindlela: Okuphakathi kanye Nemodi
Ezimweni lapho idatha iqukethe amanani amaningi aqatha noma angaphandle, i-median kanye ne-mode kungaba ezinye izindlela ezingcono kune-mean. Isibonelo, ekusatshalalisweni kwemali engenayo lapho ingxenye encane yabantu inemali engenayo ephezulu kakhulu, imali engenayo ephakathi izonikeza isithombe esinembile semali engenayo "ejwayelekile" kune-mean, engaphambukiswa yile mali engenayo ephezulu kakhulu.
Ukusetshenziswa Kokuguqulwa Kwedatha
Enye indlela yokunciphisa ithonya lamanani aqatha ukwenza ukuguqulwa kwedatha, njenge-logarithm noma impande yesikwele. Lokhu kuguqulwa kunganciphisa ithonya lamanani amakhulu kakhulu, okwenza isilinganiso simele kakhulu.
Isiphetho
Isilinganiso, noma isilinganiso, siyithuluzi lezibalo eliwusizo kakhulu ekuhlaziyweni kwedatha. Naphezu kwezinye izinkinga, ikakhulukazi ukuzwela kwayo emananini aqatha, isilinganiso sihlala singenye yezindlela ezisetshenziswa kakhulu zokulinganisa ukuthambekela okuphakathi. Ezimweni eziningi, ukwazi isilinganiso kunganikeza umbono ocacile nosheshayo wedatha ehlaziywayo.
Noma kunjalo, kubalulekile ukucabangela njalo umongo kanye nokusatshalaliswa kwedatha uma usebenzisa isilinganiso. Kwezinye izimo, i-median kanye nemodi kunganikeza isithombe esinembile kakhudlwana. Ngokuqonda kahle ukuthi kufanele sisebenzise nini futhi kanjani isilinganiso, singachaza idatha ngempumelelo kakhudlwana futhi senze izinqumo ezinolwazi oluthe xaxa.
