Ifomula Esheshayo Yokunquma Okuphakathi
Kuzibalo, i-median ingenye yezindlela ezisetshenziswa kakhulu zokulinganisa ukuthambekela okuphakathi, kanye ne-mean kanye nemodi. I-median inikeza inani eliphakathi lesethi yedatha ehlelekile, okusho ukuthi ingxenye yedatha iwela ngaphansi kwe-median kanti ingxenye iwela ngaphezu kwayo. Lesi sihloko sizochaza ifomula esheshayo kanye nendlela yokunquma i-median ngendlela elula ukuyiqonda, kokubili kumasethi wedatha angawodwa kanye namaqembu.
Isingeniso: Kuyini iMedian?
I-median iyinani eliphakathi kusethi yedatha ehleliwe. I-median iwusizo ikakhulukazi ezimweni lapho idatha iqukethe ama-outliers noma ukusatshalaliswa okungalingani, njengoba inikeza ukumelwa okunembe kakhulu kune-mean. I-median iqinile kakhulu, noma imelana namanani aqine kakhulu angase aphazamise isithombe sonke sesethi yedatha.
Ukuze uthole i-median, nansi izinyathelo eziyisisekelo ezivame ukulandelwa:
1. Hlela idatha kusukela kwencane kakhulu kuya kwenkulu kakhulu.
2. Nquma indawo ephakathi yedatha ehlungiwe.
I-Median yedatha eyodwa
Ake siqale ngesibonelo esilula sesethi yedatha eyodwa:
Idatha enezinombolo ezingalingani
Uma inani lamaphuzu edatha u-N liyinqaba, khona-ke i-median iyinani eliphakathi nendawo. Isibonelo, kudatha elandelayo:
``
3, 1, 4, 2, 5
``
Isinyathelo sokuqala ukuhlunga idatha:
``
1, 2, 3, 4, 5
``
Njengoba inani lokubonwa lingu-5 (okungajwayelekile), inani eliphakathi yinani elisesikhundleni sesi-3, okungukuthi u-3.
Idatha enezinombolo ezilinganayo
Ngenani elilinganayo lamaphuzu edatha, i-median iyisilinganiso samanani amabili aphakathi. Isibonelo, ngedatha elandelayo:
``
6, 4, 2, 8, 10, 12
``
Ngemva kokuhlunga, idatha iba:
``
2, 4, 6, 8, 10, 12
``
Njengoba inani ledatha lingu-6 (elilinganayo), amanani amabili aphakathi yidatha esezikhundleni zesithathu nezesine, okungu-6 no-8. Ngakho-ke,
``
Okuphakathi = (6 + 8) / 2 = 7
``
I-Median yedatha eqoqwe ngamaqembu
Idatha eqoqwe ndawonye isho ukuthi idatha yethulwa ngezikhawu noma ngezigaba. Kulolu hlobo lwedatha, i-median ibalwa kusetshenziswa ifomula eyinkimbinkimbi kancane.
Isibonelo, sinethebula elilandelayo lokusabalalisa imvamisa:
``
| Ikilasi | Imvamisa |
|————|———–|
| 0-10 | 5 |
| 10-20 | 8 |
| 20-30 | 12 |
| 30-40 | 7 |
| 40-50 | 3 |
``
Izinyathelo zokubala i-median yedatha eqoqwe yilezi ezilandelayo:
1. Nquma imvamisa ehlanganisiwe yekilasi ngalinye.
2. Thola u-N (inani eliphelele lamafrikhwensi).
3. Thola isigaba esimaphakathi ngokusebenzisa i-\( N/2 \).
4. Sebenzisa ifomula ephakathi nendawo yedatha eqoqwe ngamaqoqo.
Isinyathelo 1: Bala Imvamisa Ehlanganisiwe
``
| Ikilasi | Imvamisa | Imvamisa Ehlanganisiwe |
|————|————–|————————|
| 0-10 | 5 | 5 |
| 10-20 | 8 | 13 |
| 20-30 | 12 | 25 |
| 30-40 | 7 | 32 |
| 40-50 | 3 | 35 |
``
Isinyathelo 2: Ukubalwa Kwemvamisa
``
N = 35
``
Isinyathelo 3: Thola Ikilasi Eliphakathi
``
N/2 = 35/2 = 17.5
``
17.5 iwela esigabeni sama-frequency ahlanganisiwe angu-20-30.
Isinyathelo 4: Sebenzisa i-Median Formula
Ifomula ye-median yedatha eqoqwe ngamaqoqo ithi:
\[
I-Median = L_m + \left(\frac{\frac{N}{2} – F_c}{f_m} \right) \times c
\]
Kuphi:
– \(L_m\) = umkhawulo ophansi wesigaba esimaphakathi.
– \(N\) = inani eliphelele lamafrikhwensi.
– \(F_c\) = imvamisa ehlanganisiwe ngaphambi kwesigaba esimaphakathi.
– \(f_m\) = imvamisa yekilasi eliphakathi nendawo.
– \(c\) = ubude besikhawu sekilasi.
Ngemininingwane engenhla:
– \( L_m = 20 \)
– \( F_c = 13 \)
– \( f_m = 12 \)
– \( c = 10 \)
Faka amanani kufomula:
\[
I-Median = 20 + \kwesobunxele(\frac{17.5 – 13}{12} \kwesokudla) \izikhathi eziyi-10
= 20 + \kwesobunxele(\frac{4.5}{12} \kwesokudla) \izikhathi eziyi-10
= 20 + 0.375 \izikhathi eziyi-10
= 20 + 3.75
= 23.75
\]
Ngakho-ke, i-median yedatha engenhla ingu-\(23.75\).
Ukwenza kube lula ukubala okumaphakathi
Ngezinye izikhathi, ukukhumbula nokulandela ifomula efanele kungaba nzima. Nazi ezinye izeluleko namaqhinga okwenza inqubo ibe lula:
1. Sebenzisa Imidwebo noma Amagrafu: Ukubuka idatha ngesimo sama-histogram noma ama-polygon aphindaphindayo kungenza kube lula ukubona isigaba esimaphakathi nokuqonda ukusatshalaliswa kwedatha ngendlela eqondakala kalula.
2. Isofthiwe Nama-Calculator: Ukusebenzisa isofthiwe efana ne-Microsoft Excel, i-SPSS, noma ngisho ne-statistical calculator kungenza kube lula ukubala. Iningi lalezi zinhlelo zesofthiwe linikeza umsebenzi ophakathi ongasetshenziswa ngqo.
3. Ukuzijwayeza Okuvamile: Ukwenza ukuzijwayeza okuvamile ngamasethi edatha ahlukahlukene kuzokwenza ujwayelane kakhudlwana nenqubo.
4. I-Algorithm Elungisiwe: Ukuthuthukisa i-algorithm elungisiwe elandelwa njalo ukuze kutholakale i-median kuvimbela amathuba amaphutha ekubalweni.
Isiphetho
Ukunquma i-median, kungakhathaliseki ukuthi isethi yedatha eyodwa noma isethi yedatha eqoqwe ngamaqoqo, kuyikhono elibalulekile kwizibalo. Ukuqonda okuqinile kwe-median kukusiza ukuthi wenze iziphetho ezinembe kakhulu kusuka kudatha, ikakhulukazi ezimweni lapho ukusatshalaliswa kwedatha kungavamile noma kuqukethe izinto ezingaphandle. Ngokuqonda izinyathelo eziyisisekelo, ifomula efanele, kanye namaqhinga ambalwa okwenza kube lula, unganquma i-median ngokushesha nangendlela ephumelelayo. Ngethemba ukuthi lesi sihloko sinikeza ukuqonda okucacile futhi sikusize ube yingcweti yobuchwepheshe bokunquma i-median.
