Daga Bambancin Yanayi zuwa Daidaiton Bambanci
A darasi na baya, mun koyi bambancin yanayi (variance) - yadda ake auna tarwatsewar bayanai. Amma bambancin yanayi yana cikin "darajoji daidaitattun" saboda mun daidaita (square) bambance-bambancen. Misali, idan muna auna nauyi a kilo, bambancin yanayi yana cikin "kilo-daidaitattun" - wannan ba shi da ma'ana mai sauki.
Daidaiton bambanci (standard deviation) yana warware wannan matsalar ta hanyar daukar tushen murabba'i (square root) na bambancin yanayi. Wannan yana mayar da ma'aunin zuwa asalin ma'aunin bayanan - idan muna auna a kilo, daidaiton bambanci ma a kilo yake.
Menene Daidaiton Bambanci Ke Nufi?
A takaice: daidaiton bambanci yana gaya maka, a matsakaice, yaya nisan kowane daraja daga matsakaicin. Mafi karancin daidaiton bambanci, mafi kusancin darajoji zuwa juna. Mafi girmansa, mafi tarwatsewar darajoji.
Farashin kilo na naman sa a rumfuna 5 a kasuwar Kano:
₦3,500, ₦3,600, ₦3,500, ₦3,400, ₦3,500
Matsakaici = ₦3,500. Daidaiton bambanci ≈ ₦63
Farashi sun kusa da juna sosai - tarwatsewar ₦63 kawai ce.
Yanzu kwatanta da farashin a birrane daban-daban:
₦2,800, ₦3,500, ₦4,200, ₦3,000, ₦4,000
Matsakaici = ₦3,500. Daidaiton bambanci ≈ ₦554
Ko da duka matsakaicinsu daya ne, na biyu yana da tarwatsewar da ta fi girma sosai.
Ka'idar 68-95-99.7
Idan bayananku suna bin rarraba na al'ada (kwandon kararrawa), akwai ka'ida mai karfi da ake kira ka'idar 68-95-99.7:
- Kashi 68% na bayanai suna cikin daidaiton bambanci 1 daga matsakaicin
- Kashi 95% suna cikin daidaiton bambanci 2
- Kashi 99.7% suna cikin daidaiton bambanci 3
Makin JAMB na shekarar 2025: matsakaici = 220, daidaiton bambanci = 45.
- Kashi 68% na dalibai: maki 175 zuwa 265
- Kashi 95%: maki 130 zuwa 310
- Kashi 99.7%: maki 85 zuwa 355
Dalibi mai maki 320 yana cikin kashi 5% mafi girma. Dalibin da ya sami 85 yana cikin kashi 0.15% mafi karanci. Ka'idar tana ba ka hanyar tantance inda mutum yake a cikin dukan dalibai.
Daidaiton Bambanci a Lafiya
Ma'aikatan lafiya suna amfani da daidaiton bambanci don sanin abin da ke "na al'ada" da kuma abin da ke "mai ban mamaki."
Matsakaicin matsin jini na systolic a asibitin Murtala Muhammad: 120 mmHg, daidaiton bambanci: 15 mmHg.
- Matsin jini na 120 = daidai da matsakaicin (na al'ada)
- Matsin jini na 135 = daidaiton bambanci 1 sama da matsakaicin (har yanzu cikin kewayo na al'ada)
- Matsin jini na 150 = daidaiton bambanci 2 sama (na iya zama abin damuwa)
- Matsin jini na 165 = daidaiton bambanci 3 sama (mai ban mamaki, bukatar bincike)
Likitoci suna amfani da irin wannan tunanin don tantance ko gwajin mara lafiya yana cikin kewayo na al'ada ko yana bukatar karin kulawa.
Daidaiton Bambanci a Kasuwanci
Mai masana'antar chin-chin a Kano yana so ya tabbatar da ingancin kayansa. Kowane fakiti ya kamata ya yi nauyin gram 250. Ya auna fakitoci 100:
- Matsakaici: gram 251
- Daidaiton bambanci: gram 3
Idan fakiti ya yi nauyin gram 260 (daidaiton bambanci 3 daga matsakaicin), wannan na iya nufin matsalar na'ura. Amma fakiti mai nauyin gram 254 (daidaiton bambanci 1 daga matsakaicin) abu ne na al'ada.
Kwatanta Tarwatsewar: Coefficient of Variation
Wani lokaci kana bukatar kwatanta tarwatsewar abubuwa biyu da ke da ma'aunai daban-daban. Coefficient of variation (CV) yana taimaka - yana nuna daidaiton bambanci a matsayin kashi na matsakaicin:
CV = (Daidaiton Bambanci ÷ Matsakaici) × 100%
Kwatanta tarwatsewar nauyin gyada da shinkafa:
- Gyada: Matsakaici = kilo 50, Daidaiton bambanci = kilo 5. CV = 10%
- Shinkafa: Matsakaici = kilo 25, Daidaiton bambanci = kilo 4. CV = 16%
Ko da daidaiton bambancin gyada ya fi girma (5 > 4), shinkafa ce ta fi tarwatsewar idan aka yi la'akari da girmanta (16% > 10%).
Karin Misali: Daidaiton Bambanci a Wasanni
'Yan wasan NPFL biyu a kakar wasa daya:
- Dan wasa A: Kwallaye a wasanni 10: 1, 2, 1, 2, 1, 2, 1, 2, 1, 2. Matsakaici = 1.5, Daidaiton bambanci ≈ 0.53
- Dan wasa B: Kwallaye a wasanni 10: 0, 0, 5, 0, 0, 4, 0, 0, 6, 0. Matsakaici = 1.5, Daidaiton bambanci ≈ 2.22
Duka suna cin kwallaye 1.5 a matsakaice. Amma Dan wasa A yana da daidaito - koyaushe kwallo 1 ko 2. Dan wasa B yana da tsalle-tsalle - wani lokaci 0, wani lokaci 5 ko 6. Kocin da ke son dan wasa mai dogaro zai zabi A.
Daidaiton bambanci (standard deviation) yana gaya maka matsakaicin nisan kowane daraja daga matsakaicin, a ma'aunin asalin bayanan. Mafi karancin daidaiton bambanci, mafi kusancin bayanai zuwa juna. Ka'idar 68-95-99.7 tana ba ka hanyar sauri ta fahimtar yadda bayanai suka bazu a rarraba na al'ada. Ana amfani da daidaiton bambanci a lafiya don tantance abin da ke na al'ada, a kasuwanci don sarrafa inganci, kuma a rayuwar yau da kullum don kimanta dogaro da daidaito.