Indlela Yokunquma Isilinganiso Noma Isilinganiso Kusethi Yedatha
Isilinganiso singenye yezindlela ezisetshenziswa kakhulu zokulinganisa ukuthambekela okuphakathi kwezibalo, izibalo, kanye nokuphila kwansuku zonke. Uma umuntu ethi "ibanga eliphakathi lekilasi" noma "izindleko ezimaphakathi zenyanga," empeleni usho isilinganiso. Lo mqondo usisiza ukuqonda isithombe esiphelele sesethi yedatha ngokufingqa amanani amaningi abe inombolo eyodwa, emele. Kodwa-ke, nakuba kungase kuzwakale kulula, ukunquma isilinganiso kudinga izinyathelo eziqondile, ikakhulukazi lapho idatha inamafomethi ahlukene, njengedatha eyodwa, idatha yemvamisa, noma idatha eqoqwe. Lesi sihloko sichaza indlela yokunquma isilinganiso kusethi yedatha ngokucacile, ngezibonelo zokwenza kube lula ukuyiqonda.
Ukuqonda Isilinganiso (Isilinganiso)
Isilinganiso yinani elitholakala ngokungeza yonke idatha bese uyihlukanisa ngenani lamaphuzu edatha. Isilinganiso sivame ukusetshenziswa ngoba kulula ukubala futhi singamelela ukuthambekela okuvamile kwesethi yedatha. Ekubhalweni kwezibalo, isilinganiso sivame ukubhalwa ngophawu \(\bar{x}\) (olubizwa ngokuthi "x bar").
Ifomula ejwayelekile yesilinganiso sedatha eyodwa yile:
\[
\bar{x} = \frac{\sum x}{n}
\]
Imininingwane:
– \(\isamba x\) = isamba sawo wonke amanani edatha
– \(n\) = inani ledatha
Ngamanye amazwi, isilinganiso “inani eliphelele” elihlukaniswe “inani lamanani”.
1. Ukunquma isilinganiso kudatha eyodwa
Isethi yedatha eyodwa iyisethi yamanani abhalwe njengoba enjalo, ngaphandle kokufakwa kuhlu lwemvamisa. Ukubala isilinganiso kusethi yedatha eyodwa kulula kakhulu.
Isibonelo:
Amaphuzu okuhlolwa kwezibalo abafundi abahlanu ayengu: 70, 80, 75, 85, 90.
Bala isilinganiso.
Isinyathelo:
1. Hlanganisa wonke amanani:
70 + 80 + 75 + 85 + 90 = 400
2. Bala idatha eningi:
n = 5
3. Hlukanisa inani ledatha ngenani ledatha:
\(\ibha{x} = 400 / 5 = 80\)
Ngakho-ke, inani eliphakathi lingu-80.
Amathiphu abalulekile:
– Qiniseka ukuthi yonke idatha ifakwe kahle.
– Ungakhohlwa ukubala inani ledatha ngokucophelela, ikakhulukazi uma idatha iningi kakhulu.
2. Ukunquma isilinganiso kudatha yemvamisa
Ngezinye izikhathi idatha ayiboniswa ngayinye, kodwa iboniswa njengenani kanye nemvamisa yayo (inani livela kangaki). Lokhu kubizwa ngokuthi idatha yemvamisa. Kulesi simo, asingezi amanani ngamanye, kodwa kunalokho siphinda inani ngemvamisa.
Ifomula ephakathi yedatha evame kakhulu:
\[
\bar{x} = \frac{\sum (x \cdot f)}{\sum f}
\]
Imininingwane:
– \(x\) = inani ledatha
– \(f\) = ukuvama kokwenzeka kwenani
– \(\sum (x \cdot f)\) = isamba semiphumela yokuphindaphinda inani kanye nemvamisa
– \(\sum f\) = imvamisa iyonke (inani eliphelele ledatha)
Isibonelo:
Ithebula lamanani kanye nemvamisa:
| Inani (x) | Imvamisa (f) |
|———-:|—————–:|
| 60 | 2 |
| 70 | 3 |
| 80 | 4 |
| 90 | 1 |
Bala isilinganiso.
Isinyathelo:
1. Bala umugqa ngamunye:
- 60 × 2 = 120
- 70 × 3 = 210
- 80 × 4 = 320
- 90 × 1 = 90
2. Hlanganisa imiphumela:
\(\isamba (x \cdot f) = 120 + 210 + 320 + 90 = 740\)
3. Hlanganisa wonke amaza:
\(\isamba f = 2 + 3 + 4 + 1 = 10\)
4. Yabelana:
\(\ibha{x} = 740 / 10 = 74\)
Ngakho-ke isilinganiso sedatha singama-74.
3. Ukunquma Isilinganiso Kudatha Eqoqwe (Isikhawu Sekilasi)
Ngemininingwane eminingi, ivame ukuhlukaniswa ngezikhawu zekilasi, njengo-50–59, 60–69, njalo njalo. Lokhu kubizwa ngokuthi idatha eqoqwe ndawonye. Ukuze sibale isilinganiso sedatha eqoqwe ndawonye, sisebenzisa i-midpoint (inani eliphakathi nendawo) yekilasi ngalinye njengesethi yedatha emele.
Ifomula yesilinganiso sedatha eqoqwe ngamaqoqo:
\[
\bar{x} = \frac{\sum (x_i \cdot f_i)}{\sum f_i}
\]
Imininingwane:
– \(x_i\) = isigaba esiphakathi nendawo
– \(f_i\) = imvamisa yekilasi
Indlela yokuthola indawo ephakathi:
\[
x_i = \frac{\text{lower bound} + \text{upper bound}}{2}
\]
Isibonelo:
Ithebula ledatha eliqoqwe ngamaqoqo:
| Isikhawu | Imvamisa (f) |
|———:|—————–:|
| 50–59 | 4 |
| 60–69 | 6 |
| 70–79 | 8 |
| 80–89 | 2 |
Isinyathelo:
1. Thola indawo ephakathi nendawo yesikhawu ngasinye:
– 50–59 → \((50+59)/2 = 54,5\)
– 60–69 → \((60+69)/2 = 64,5\)
– 70–79 → \((70+79)/2 = 74,5\)
– 80–89 → \((80+89)/2 = 84,5\)
2. Phindaphinda i-midpoint ngemvamisa yayo:
- 54,5 × 4 = 218
- 64,5 × 6 = 387
- 74,5 × 8 = 596
- 84,5 × 2 = 169
3. Hlanganisa konke:
\(\isamba (x_i f_i) = 218 + 387 + 596 + 169 = 1370\)
4. Hlanganisa amaza:
\(\isamba f = 4 + 6 + 8 + 2 = 20\)
5. Bala isilinganiso:
\(\ibha{x} = 1370 / 20 = 68,5\)
Ngakho-ke isilinganiso sedatha eqoqwe ngamaqoqo singu-68,5.
4. Izinto Okufanele Uziqaphele Lapho Ubala Isilinganiso
Nakuba ifomula ephakathi ibonakala ilula, kunezinto eziningana ezibalulekile ukuqinisekisa imiphumela yokubala enembile:
1. Isilinganiso sinozwela ezintweni ezibaluleke kakhulu
Uma kunenani elikhulu kakhulu noma elincane kakhulu (elingaphandle), isilinganiso singashintsha kakhulu. Isibonelo, imali engenayo ejwayelekile izokwenyuka uma umuntu oyedwa enomholo ophezulu kakhulu.
2. Qiniseka ukuthi uhlobo lwedatha lulungile
Isilinganiso sifanele idatha yezinombolo (izinombolo). Kudatha yezigaba ezifana "nombala owuthandayo" noma "uhlobo lwemoto," isilinganiso asikwazi ukusetshenziswa.
3. Sebenzisa ukuzungeza njengoba kudingeka
Kudatha eqoqwe ngamaqoqo, isilinganiso sivame ukuba yidesimali. Sondeza isilinganiso njengoba kudingeka (isb., ezindaweni ezimbili zedesimali).
4. Hlola imvamisa iyonke futhi
Kudatha yemvamisa noma eqoqwe ngamaqoqo, iphutha elivamile ukwengeza amamvamisa ngendlela engafanele, okuholela ekuhlukaniseni okungalungile.
5. Ukusetshenziswa kwe-Mean Empilweni Yansuku Zonke
I-Mean ayisetshenziswa kuphela ezifundweni zezibalo, kodwa futhi nasezindaweni ezahlukene:
– Imfundo: nquma isilinganiso samaphuzu okuhlolwa kwabafundi.
– Ezomnotho: ukubala imali engenayo emaphakathi, intengo emaphakathi yezimpahla.
– Impilo: isilinganiso somfutho wegazi, isilinganiso samakhalori okusetshenziswa.
– Ezemidlalo: amaphuzu aphakathi ngomdlalo ngamunye.
– Ibhizinisi: isilinganiso sokuthengisa kwansuku zonke noma kwanyanga zonke.
Ngokuqonda isilinganiso, singenza izinqumo ngokusekelwe kudatha ngendlela enengqondo nelinganisekayo.
Isiphetho
Ukunquma isilinganiso noma isilinganiso sesethi yedatha kungenziwa ngezindlela eziningana, kuye ngohlobo lwedatha. Kumasethi edatha angawodwa, isilinganiso sitholakala ngokuhlukanisa inani lamasethi edatha ngenani lamasethi edatha. Kumasethi edatha yemvamisa, isamba samanani aphindaphindwe ngamaza awo sihlukaniswa yimvamisa iyonke. Kumasethi edatha aqoqwe ngamaqoqo, isilinganiso sibalwa ngokusebenzisa i-midpoint yesikhawu ngasinye sekilasi njengesethi yedatha emele. Ngokulandela izinyathelo ezifanele neziqondile, isilinganiso singaba ithuluzi eliwusizo kakhulu lokuqonda nokuhlaziya idatha ezimweni ezahlukahlukene.
Uma ungathanda, ngingenza futhi inguqulo "yesitayela sebhulogi" (ekhululekile kakhudlwana) yalesi sihloko, noma ngengeze imibuzo yokuzijwayeza nezimpendulo ukuze kube lula ukuyiqonda.
