Menene "Matsakaici"?
Sa'ad da wani ya ce "matsakaicin farashin shinkafa" ko "matsakaicin makin jaraba," yana kokarin bayyana dukan gungun lambobi da lamba guda daya. Wannan lambar daya tana wakiltar abin da ke "na yau da kullum" ko "na al'ada."
Amma ga abin da mafi yawan mutane ba su sani ba: akwai hanyoyi fiye da daya na lissafa matsakaici. Hanyoyi uku mafi sani sune matsakaici (mean), tsakiya (median), da yanayi (mode). Kowanne yana ba da labari daban, kuma zabin wanda ya dace yana da muhimmanci.
Matsakaici (Mean): Hada Komai Ka Raba
Matsakaici shine abin da mafi yawan mutane ke tunani sa'ad da suka ji "average." Ka hada dukan lambobi ka raba da adadin lambobin.
Dalibai biyar sun kwatanta makinsu na JAMB: 210, 245, 260, 280, 305.
Mataki na 1: Ka hada su: 210 + 245 + 260 + 280 + 305 = 1,300
Mataki na 2: Ka raba da 5 (saboda lambobi 5 ne): 1,300 ÷ 5 = 260
Matsakaicin makin JAMB shine 260.
Matsakaici yana aiki ne idan lambobi suna kusa da juna kuma babu darajoji matsananciya da ke jan shi wani bangare. Yana amfani da kowace lamba a lissafin, wannan shi ne karfinsa da kuma rauninsa.
Sa'ad da Matsakaici Ya Karkace
Ka yi tunanin kana kallon kudin shiga na ma'aikata a wani kantin sayar da kaya a Kano:
Kudin shigan ma'aikata: ₦45,000 · ₦50,000 · ₦55,000 · ₦60,000 · ₦500,000
Matsakaicin kudin shiga: (₦45,000 + ₦50,000 + ₦55,000 + ₦60,000 + ₦500,000) ÷ 5 = ₦142,000
Shin ₦142,000 yana wakiltar abin da ma'aikaci na yau da kullum ke samu? A'a sam. Ma'aikata hudu cikin biyar suna samun kasa da haka sosai. Babban kudin shigan - mai kantin watakila - ya ja matsakaicin sama sosai.
Tsakiya (Median): Lambar da ke Tsakanin
Tsakiya ita ce lambar da ke tsakiya sa'ad da ka jera dukan darajoji daga mafi karanci zuwa mafi girma. Rabinta suna kasa da ita, rabinta suna sama da ita.
Kudin shiga na ma'aikata, a jere: ₦45,000 · ₦50,000 · ₦55,000 · ₦60,000 · ₦500,000
Tsakiya ita ce ₦55,000 - lambar da ke tsakiya daidai.
Wannan hoto ne mafi kyau na abin da ma'aikaci na al'ada ke samu a wannan kantin.
Idan Lambobi Cuku-cuku Ne Fa?
Sa'ad da kana da lambobi masu yawan cuku-cuku (even number), babu lambar tsakiya daya. A wannan halin, ka dauki lambobi biyu na tsakiya ka nemo matsakaicinsu.
Farashin tumatir a rumfuna 6 a kasuwar Yankaba: ₦300, ₦350, ₦400, ₦450, ₦500, ₦550
Lambobi biyu na tsakiya su ne ₦400 da ₦450. Matsakaicinsu: (₦400 + ₦450) ÷ 2 = ₦425
Tsakiya ita ce ₦425.
Tsakiya ba ta canzawa saboda darajoji matsananciya. Ko da babban kudin shiga a misalinmu na baya ya kasance ₦5,000,000 maimakon ₦500,000, tsakiya za ta kasance ₦55,000. Wannan yana sa ta zama da amfani musamman sa'ad da bayananku ke da darajoji masu tsayin daka.
Yanayi (Mode): Lambar da Ta Fi Bayyana
Yanayi shine darajar da ta fi bayyana sau da yawa. Shine mafi saukin ra'ayi a cikin ukun, kuma yana aiki da kowace irin bayanai - har da wadanda ba lambobi ba.
Mai sayar da takalma a Kano ya bi diddigin girman da ake fi sayarwa a mako guda: 42, 43, 43, 44, 43, 45, 42, 43, 44, 43
Girman 43 ya bayyana sau 5 - fiye da kowanne. Yanayin shine girman 43.
Wannan bayani ne mai amfani. Ya kamata ya tabbatar cewa yana da isassun takalmin girman 43 a rumfarsa.
Yanayi yana aiki da rukunoni ma. Idan bincike ya tambayi mutane abincin da suka fi so kuma "tuwo" ya fi kowanne, to tuwo shine yanayin.
Shin Za a Sami Yanayi Fiye da Daya?
Eh. Idan darajoji biyu sun daidaita a mafi yawan bayyanar, kana da yanayi biyu (bimodal). Idan duk daraja ta bayyana yawan daya, babu yanayi kwata-kwata.
Kwatanta Su Uku: Kallon Gefe da Gefe
Adadin kwallaye da dan wasan NPFL ya ci a wasanni 9: 0, 1, 1, 1, 2, 2, 3, 3, 5
Matsakaici (Mean): (0+1+1+1+2+2+3+3+5) ÷ 9 = 18 ÷ 9 = kwallaye 2
Tsakiya (Median): Lambar ta 5 (tsakiyar 9) = kwallaye 2
Yanayi (Mode): 1 ya bayyana sau 3 = kwallo 1
A nan, ukun suna kusa da juna. Dan wasan da ya ci 5 a wasa daya ya ja matsakaicin sama kadan, amma ba sosai ba.
Yaushe Za Ka Yi Amfani da Kowanne?
Yi amfani da matsakaici sa'ad da: bayananku ba su da darajoji matsananciya kuma sun bazu daidai. Shine mafi yawan abin da ake amfani da shi a bincike na kimiyya.
Yi amfani da tsakiya sa'ad da: bayananku suna da darajoji matsananciya ko sun karkata zuwa wani bangare. Shi ya sa rahoton NBS game da kudin shigan iyali yakan yi amfani da tsakiya - 'yan attajirai kadan za su sa matsakaicin ya zama maras gaskiya.
Yi amfani da yanayi sa'ad da: kana son sanin zabin da ya fi shahara. Yana da amfani musamman don rukunoni (launi da aka fi so, kayan da aka fi saya) da kuma yanke shawara na kasuwanci kamar nawa kaya ne za ka ajiye.
Tarkon da Za Ka Kula Da Shi
Sa'ad da ka ga kalmar "matsakaici" a labarin jarida, talla, ko rahoto, ka tambayi kanka: wanne matsakaici? Kamfani na iya tallata cewa ma'aikatansu suna samun "matsakaicin kudin shiga na ₦250,000" ta amfani da mean - wanda daraktocin kamfani ke ja sama - yayin da tsakiya (median) na iya kasancewa ₦85,000. Duk lambobi biyu daidai ne a kimiyance, amma suna ba da labarai daban-daban.
Matsakaici (mean) yana hada dukan darajoji ya raba da adadin - yana da amfani amma darajoji matsananciya suna shafe shi. Tsakiya (median) tana zaban lambar tsakiya - ta fi kyau sa'ad da akwai darajoji matsananciya. Yanayi (mode) yana gano mafi yawan bayyanar - yana aiki da kowace irin bayanai. Sanin wanne za ka yi amfani da shi (da kuma wanne wani ya zaba ya yi amfani da shi) yana taimaka maka ka fahimci abin da lambobi ke fada a zahiri.