Matekiniki ekuwana Median yeData: Gwaro Rakazara
Muchidimbu, musanganiswa wepakati (median) chinhu chakakosha zvikuru pakuyera tsika yepakati muhuwandu hwedata. Muchidimbu, musanganiswa wepakati (median) ndiwo muganho wepakati mudata kana data rakarongedzwa nehukuru hwaro. Kunzwisisa maverengerwo emusanganiswa wepakati (median) hunyanzvi hwekutanga hwehuwandu hunokosha, mukuongorora data redzidzo uye munyika yehunyanzvi. Chinyorwa chino chichakurukura matekiniki akasiyana-siyana ekutsvaga musanganiswa wepakati mumhando dzakasiyana dzedata uye kupa mienzaniso yakadzama kuti zvive nyore kunzwisisa.
Chii chinonzi Median?
Mupakati ndiyo nzvimbo iri pakati pedata rakarongeka. Kana nhamba yemapoinzi edata iri odd, mupakati ndiyo kukosha kwepakati. Kana nhamba yemapoinzi edata iri even, mupakati ndiyo avhareji yemapoinzi maviri epakati ari mumapoinzi edata. Mupakati akasiyana neavhareji pakuti haakanganisike nemapoinzi akawandisa (extreme values (outliers).
Matanho Ekuverenga Pakati
Kune matanho anoverengeka ekutanga ekutevera kuti uverenge median:
1. Kuronga Data:
Data rinofanira kurongwa kubva padiki kusvika pahukuru.
2. Sarudza Huwandu hweData:
Verenga huwandu hwezvinhu zviri mudataset (n).
3. Kusarudza Nzvimbo Yepakati:
– Kune nhamba isina kujairika yedata: Nzvimbo yepakati ndiyo [(n+1)/2]th value.
– Kune nhamba yakaenzana yedata: Avhareji ndiyo avhareji yemitengo miviri iri munzvimbo dze [n/2]th uye [(n/2)+1].
Ngatitsanangure matanho aya nemuenzaniso chaiwo.
Muenzaniso weData Risingawanzoonekwi
Ngatitii tine data risinganzwisisike: [3, 1, 5, 7, 9]
1. Kuronga Data:
Mushure mekuronga, seti yedata inova: [1, 3, 5, 7, 9]
2. Sarudza Huwandu hweData:
n = 5
3. Kusarudza Nzvimbo Yepakati:
Sezvo nhamba yedata isina kurongeka (5), nzvimbo yepakati ndiyo [(5+1)/2] = kukosha kwechitatu.
Saka, avhareji yedata reseti i5.
Muenzaniso weData rakafanana
Ngatitii tine data rakafanana: [8, 3, 7, 5, 10, 2]
1. Kuronga Data:
Mushure mekuronga, seti yedata inova: [2, 3, 5, 7, 8, 10]
2. Sarudza Huwandu hweData:
n = 6
3. Kusarudza Nzvimbo Yepakati:
Sezvo nhamba yedata yakaenzana (6), iyo iri pakati ndiyo avhareji yenhamba mbiri dzepakati, dzinoti [6/2] = kukosha kwechitatu uye [(6/2)+1] = kukosha kwechina.
Aya manhamba ndi5 na7. Saka, avhareji = (5+7)/2 = 6.
Pakati peData Rakaunganidzwa
Kana uchibata nedata rakabatanidzwa kana data rakarongwa muzvikamu, kuverenga median kwakaoma zvishoma asi kunogona kuitwa nenzira yakarongeka.
Ngatitii tine tafura yekugoverwa kwema frequency iri pazasi:
| Nguva | Nguva Yakawanda |
| ——– | ——— |
| 0-10 | 5 |
| 10-20 | 8 |
| 20-30 | 12 |
| 30-40 | 10 |
| 40-50 | 6 |
1. Tsvaga Kuwanda Kwakawanda:
| Nguva | Kuwanda (f) | Kuwanda Kwakawanda (F) |
| ——– | ————- | ———————– |
| 0-10 | 5 | 5 |
| 10-20 | 8 | 13 |
| 20-30 | 12 | 25 |
| 30-40 | 10 | 35 |
| 40-50 | 6 | 41 |
2. Kuziva Nzvimbo Yepakati:
N = huwandu hwemafrequencies = 41. Pakati pepakati iri panzvimbo (N/2) = 41/2 = 20,5.
3. Kuziva Pakati Penguva:
Chikamu chine nzvimbo ye20,5th i20-30.
4. Kushandisa Fomura Yepakati:
Iyo yepakati yedata rekirasi inotsanangurwa nefomula:
\[
\text{Median} = L + \left( \frac{\left( \frac{N}{2} – F_{c-1} \right)}{f_m} \right) \times i
\]
Di mana:
– \( L \) ndiwo muganho wakaderera wekirasi yepakati.
– \( N \) ndiyo nhamba yese yemafrequencies.
– \( F_{c-1} \) ndiyo frequency inounganidzwa isati yasvika pakati pekirasi.
– \( f_m \) ndiyo frequency yepakati pekirasi.
– \( i \) upamhi hwechikamu chekirasi.
Kubva padata:
– \( L = 20 \)
– \( N = 41 \)
– \( F_{c-1} = 13 \) (kuwanda kwehuwandu hwekuverenga usati wasvika kirasi 20-30)
– \( f_m = 12 \)
– \( i = 10 \) (upamhi hwepakati)
Saka:
\[
\text{Median} = 20 + \left( \frac{(20,5 – 13)}{12} \right) \times 10 = 20 + \left( \frac{7,5}{12} \right) \times 10 = 20 + 6,25 = 26,25
\]
Pakati peData reCategorical
Padata remapoka kana reordinal, median inogona kuverengerwa nekuona nzvimbo yechinhu chinoparadzanisa data rakarongeka kuita zvikamu zviviri zvakaenzana.
Semuenzaniso, data rinotevera ipfungwa yekugutsikana kwemushandisi: [Zvakaipa, Zvakanaka, Zvakanaka, Zvakanaka Kwazvo, Zvakanaka, Zvakanaka]
1. Kuronga Data:
Kuronga zvine musoro nekuongorora: [Zvakaipa, Zvakanaka, Zvakanaka, Zvakanaka, Zvakanaka, Zvakanaka Kwazvo]
2. Sarudza Huwandu hweData:
n = 6
3. Kuziva Pakati:
Sezvo nhamba yedata yakaenzana (6), avhareji ndiyo avhareji yenhamba mbiri dzepakati, dzinoti [6/2] = 3rd uye (6/2 + 1) = nhamba dzechina.
Aya ma "Vakakwana" uye "Vakanaka." Nekuti iyi idata remapoka, hatigone kutora avhareji yenhamba, saka tinowanzo tora kukosha kuri pakati kwakakodzera mamiriro acho ezvinhu, semuenzaniso, tichishandisa ordinal interpolation.
Mhedziso
Kuwana nzira yepakati inzira yakakosha mukuongorora nhamba. Nzira yepakati inopa ruzivo nezve seti yedata isina kukanganiswa nehukuru hwakanyanya. Nzira inoshandiswa inoenderana nerudzi rwedata rauinaro—ingave iri imwe chete, yakarongwa, kana kuti yakarongwa. Nekutevera matanho akarongwa pamusoro apa, unogona kuwana nyore nyore nzira yepakati yemaseti akasiyana-siyana edata. Izvi hazvingokubatsiri chete kunzwisisa kugoverwa kwedata rako asiwo zvichakubatsira kuita sarudzo dzine ruzivo rwakawanda zvichibva pairi.
