Fomura Inokurumidza Yekuona Pakati
Muhuwandu hwehuwandu, medium ndeimwe yenzira dzinoshandiswa zvakanyanya dzepakati, pamwe chete ne mean uye mode. Median inopa kukosha kwepakati kweseti yedata rakarongwa, zvichireva kuti hafu yedata inowira pasi pe median uye hafu inowira pamusoro payo. Chinyorwa chino chichatsanangura fomura nekukurumidza uye nzira yekuona median nenzira iri nyore kunzwisisa, kune ese ari maviri data sets uye mapoka data.
Nhanganyaya: Chii chinonzi Median?
Mupakati ndiwo mutengo wepakati uri museti yedata yakarongeka. Mupakati unonyanya kubatsira mumamiriro ezvinhu apo data rine zvinhu zvisingaenzaniswi kana kugoverwa kusina kuenzana, sezvo richipa mufananidzo wakarurama kupfuura avhareji. Mupakati wacho wakasimba, kana kuti unodzivirira kukoshesa kwakanyanya kunogona kukanganisa mufananidzo wese weseti yedata.
Kuti uone kuti muvhareji wepakati, heano matanho ekutanga anowanzo teverwa:
1. Ronga data kubva padiki kusvika pakuru.
2. Sarudza nzvimbo yepakati yedata rakarongeka.
Pakati peData Rimwe Chete
Ngatitangei nemuenzaniso uri nyore weseti imwe chete yedata:
Data rine Nhamba Dzisina Kurongeka
Kana nhamba yemapoinzi edata N isina kuenzana, zvinoreva kuti median ndiyo kukosha kuri pakati. Semuenzaniso, kune data rinotevera:
``
3, 1, 4, 2, 5
``
Danho rekutanga nderekugadzirisa data:
``
1, 2, 3, 4, 5
``
Sezvo nhamba yezvakaonekwa iri 5 (zvisingawanzoitiki), kukosha kwepakati ndiko kukosha kuri panzvimbo yechitatu, kureva 3.
Data rine Nhamba Dzakaenzana
Kune nhamba yakaenzana yedata points, median ndiyo avhareji yemitengo miviri yepakati. Semuenzaniso, kune data rinotevera:
``
6, 4, 2, 8, 10, 12
``
Mushure mekuronga, data rinova:
``
2, 4, 6, 8, 10, 12
``
Sezvo nhamba yedata iri 6 (yakaenzana), manhamba maviri epakati ndiwo data riri munzvimbo yechitatu neyechina, kureva 6 ne8. Saka,
``
Pakati = (6 + 8) / 2 = 7
``
Pakati peData Rakaunganidzwa
Data rakarongwa mumapoka zvinoreva kuti data rinounzwa muzvikamu kana muzvikamu. Pamhando iyi yedata, median inoverengwa uchishandisa fomura yakaoma zvishoma.
Semuenzaniso, tine tafura yekugoverwa kwema frequency inotevera:
``
| Kirasi | Kuwanda |
|————|———–|
| 0-10 | 5 |
| 10-20 | 8 |
| 20-30 | 12 |
| 30-40 | 7 |
| 40-50 | 3 |
``
Matanho ekuverenga medium yedata rakabatanidzwa ndeaya anotevera:
1. Sarudza huwandu hwekuverenga hunowanikwa mukirasi yega yega.
2. Sarudza N (huwandu hwemafrequencies).
3. Tsvaga kirasi yepakati kuburikidza ne \( N/2 \).
4. Shandisa fomura yepakati yedata rakarongwa.
Danho 1: Verenga Kuwanda Kwakawanda
``
| Kirasi | Kuwanda | Kuwanda Kwakawanda |
|————|————–|————————|
| 0-10 | 5 | 5 |
| 10-20 | 8 | 13 |
| 20-30 | 12 | 25 |
| 30-40 | 7 | 32 |
| 40-50 | 3 | 35 |
``
Danho rechipiri: Kuverengwa kweManguva
``
N = 35
``
Danho rechitatu: Tsvaga Kirasi yepakati
``
N/2 = 35/2 = 17.5
``
17.5 inowira muchikamu che cumulative frequency class 20-30.
Danho rechina: Shandisa Median Formula
Fomura yepakati pedata rakabatanidzwa ndeiyi:
\[
Pakati = L_m + \left(\frac{\frac{N}{2} – F_c}{f_m} \right) \times c
\]
Dimana:
– \(L_m\) = muganho wakaderera wekirasi yepakati.
– \(N\) = huwandu hwese hwemafrequencies.
– \(F_c\) = cumulative frequency isati yasvika padanho repakati.
– \(f_m\) = frequency yepakati pekirasi.
– \(c\) = kureba kwechikamu chekirasi.
Kune data riri pamusoro apa:
– \( L_m = 20 \)
– \( F_c = 13 \)
– \( f_m = 12 \)
– \( c = 10 \)
Tsiva ma "values" mufomura:
\[
Pakati = 20 + \kuruboshwe(\frac{17.5 – 13}{12} \kurudyi) \kawa 10
= 20 + \kuruboshwe(\frac{4.5}{12} \kurudyi) \kawa 10
= 20 + 0.375 \kawa 10
= 20 + 3.75
= 23.75
\]
Saka, muyero wepakati wedata riri pamusoro apa ndi \(23.75\).
Kurerutsa Kuverenga Kwepakati
Dzimwe nguva, kurangarira nekutevera nzira chaiyo kunogona kuoma. Heano mamwe matipi uye mazano ekuita kuti maitiro acho ave nyore:
1. Shandisa Madhayagiramu kana Magirafu: Kuona data muchimiro chehistograms kana ma frequency polygons kunogona kuita kuti zvive nyore kuona kirasi yepakati uye kunzwisisa kugoverwa kwedata zviri nyore.
2. Software neMakarukureta: Kushandisa software yakaita seMicrosoft Excel, SPSS, kana kunyange karukureta yenhamba kunogona kurerutsa kuverenga. Mazhinji emapurogiramu aya esoftware anopa basa repakati rinogona kushandiswa zvakananga.
3. Kudzidzira Nguva Dzose: Kuita kudzidzira nguva dzose uchishandisa madata akasiyana-siyana kuchaita kuti uzive zviri nani maitiro acho.
4. Fixed Algorithm: Kugadzira algorithm yakagadziriswa inoteverwa nguva dzese kuti ione kuti pakati pehuwandu hwepakati pakuverenga kunodzivirira mukana wekuti pave nezvikanganiso mukuverenga.
Mhedziso
Kuziva pakati pe data, kungave kwedata rimwe chete kana kuti boka re data, hunyanzvi hwakakosha muhuwandu hwe data. Kunzwisisa kwakasimba kwepakati kunokubatsira kuita fungidziro dzakarurama kubva pa data, kunyanya mumamiriro ezvinhu apo kugoverwa kwe data kusina kuenzana kana kuti kune zvinhu zvisingawanzoitiki. Nekunzwisisa matanho ekutanga, fomura chaiyo, uye mamwe matipi ekurerutsa, unogona kuona pakati nekukurumidza uye zvinobudirira. Tinovimba kuti chinyorwa chino chinopa nzwisiso yakajeka uye chinokubatsira kugona nzira yekuona pakati pe data.
