Matsakaici Kadai Ba Ya Isa
Ka yi tunanin makarantu biyu a Kano. Duka biyun suna da matsakaicin makin WAEC na 60 cikin 100. Shin daidai suke? Wataƙila a'a.
- Makaranta A: Makin dalibai: 55, 58, 60, 62, 65
- Makaranta B: Makin dalibai: 20, 40, 60, 80, 100
Duka biyun matsakaicinsu 60 ne, amma sun bambanta sosai. Makaranta A dalibanta suna kusa da juna. Makaranta B tana da dalibai masu makin da suka bambanta da yawa. Don fahimtar wannan bambancin, muna bukatar auna tarwatsewar bayanai - yadda lambobi suka bazu.
Kewayo (Range): Mafi Sauki
Kewayo shine bambancin da ke tsakanin daraja mafi girma da mafi karanci.
Kewayo = Mafi girma - Mafi karanci
Farashin lita na man fetur a tashoshi 5 a Kano:
₦615, ₦620, ₦625, ₦618, ₦640
Kewayo = ₦640 - ₦615 = ₦25
Wannan yana gaya maka cewa bambancin farashi ya kai ₦25 a cikin tashoshin da ka duba.
Kewayo yana da sauki amma yana da rauni: yana amfani da darajoji biyu kawai - mafi girma da mafi karanci. Idan daya daga cikinsu daraja ce matsananciya (outlier), kewayo zai zama maras gaskiya.
Kudin shigan ma'aikata a wata ofishin: ₦50,000, ₦55,000, ₦52,000, ₦58,000, ₦400,000
Kewayo = ₦400,000 - ₦50,000 = ₦350,000
Wannan kewayo yana sa a yi tunanin akwai tarwatsewar da yawa, amma a zahiri ma'aikata 4 cikin 5 suna kusa da juna. Babban kudin shigan guda daya ya tilasta wa kewayo ya zama babba.
Bambancin Yanayi (Variance): Mafi Daidai
Bambancin yanayi yana auna yadda kowane daraja ke nisa da matsakaicin, a matsakaice. Ya fi kewayo saboda yana amfani da dukan darajoji, ba biyu kawai ba.
Matakan Lissafi
- Nemo matsakaicin (mean)
- Cire matsakaicin daga kowane daraja (samun bambance-bambance)
- Daidaita kowane bambanci (ninka shi da kansa) - wannan yana kawar da lambobi mara kyau
- Nemo matsakaicin daidaitattun bambance-bambancen
Kwallaye da dan wasan Kano Pillars ya ci a wasanni 5: 1, 3, 2, 4, 0
Mataki 1: Matsakaici = (1+3+2+4+0) ÷ 5 = 10 ÷ 5 = 2
Mataki 2: Bambance-bambance daga matsakaicin:
- 1 - 2 = -1
- 3 - 2 = 1
- 2 - 2 = 0
- 4 - 2 = 2
- 0 - 2 = -2
Mataki 3: Daidaitawa (squaring):
- (-1)² = 1
- (1)² = 1
- (0)² = 0
- (2)² = 4
- (-2)² = 4
Mataki 4: Matsakaici = (1+1+0+4+4) ÷ 5 = 10 ÷ 5 = 2
Bambancin yanayi shine 2.
Matsalar Bambancin Yanayi: Daidaitawa
Ka lura da wani abu game da bambancin yanayi: saboda mun daidaita bambance-bambancen, ma'aunin ya canja. Idan mun auna kwallaye, bambancin yanayi yana cikin "kwallaye daidaitattun" - wannan ba shi da ma'ana a saukake. Hanyar warware wannan ita ce amfani da standard deviation, wanda za mu koya a darasi na gaba.
Samfurin da Al'umma: Bambancin Formula
Akwai bambanci kadan a formulan bambancin yanayi:
- Bambancin yanayi na al'umma: Ka raba da N (jimlar al'umma)
- Bambancin yanayi na samfuri: Ka raba da (n - 1) maimakon n. Wannan ana kiransa "Bessel's correction" kuma yana ba da kimantawa mafi daidai.
A misalinmu na sama, idan kwallaye biyar sune samfuri ne kawai (ba dukan wasannin ba), bambancin yanayi zai zama 10 ÷ 4 = 2.5 maimakon 2.
Me Ya Sa Tarwatsewar Ke Da Muhimmanci?
Kamfanoni biyu na sufuri suna tafiya daga Kano zuwa Abuja. Duka biyun suna cewa tafiyar tana daukar sa'o'i 8 a matsakaice. Amma:
- Kamfani A: Tafiyoyi na baya-bayan nan: sa'o'i 7.5, 8, 8.5, 7.5, 8.5 (kewayo: 1 sa'a)
- Kamfani B: Tafiyoyi na baya-bayan nan: sa'o'i 5, 12, 6, 11, 6 (kewayo: 7 sa'o'i)
Duka matsakaicinsu sa'o'i 8 ne. Amma Kamfani A yana da karancin tarwatsewar - za ka iya dogara da su. Kamfani B na iya kai ka cikin sa'o'i 5 ko kuma ya dauki sa'o'i 12. Idan kana da muhimmin aiki a Abuja, Kamfani A ya fi aminci.
Kewayo (range) yana auna bambancin tsakanin mafi girma da mafi karanci - sauki amma darajoji matsananciya suna shafe shi. Bambancin yanayi (variance) yana auna matsakaicin nisan kowane daraja daga matsakaicin - ya fi daidai saboda yana amfani da dukan bayanai. Duka biyun suna taimaka maka ka ga abin da matsakaici kadai ba zai iya nuna ba: yadda bayanai suka bazu. Mafi girman tarwatsewar, mafi karancin dogaro kan matsakaicin.