Mibvunzo Yemuenzaniso Inokurukura Nezvepakati uye Mode Kirasi yeData reBoka
Muhuwandu hwezviverengero, nzira yepakati nemodhi zviyero zviviri zvakakosha zvetsika yepakati. Muchinyorwa chino, tichakurukura zvakadzama nezvenzira yepakati nemodhi mumashoko edata rakarongwa, kusanganisira mienzaniso yakati wandei yezvinetso kuti zvikubatsire kunzwisisa.
Kunzwisisa Median uye Mode
Median
Muchidimbu zvinoreva kukosha kwepakati peseti yedata kana data rarongwa. Muchidimbu chedata rakarongwa, muchidimbu zvinoreva kirasi inokamura data kuita zvikamu zviviri zvakaenzana.
maitiro
Modhi ndiyo kukosha kana kirasi inoonekwa kakawanda museti yedata. Kune data rakarongwa, modhi ndiyo kirasi ine frequency yepamusoro.
Kuverenga Median neMode Class yeData Rakaunganidzwa
Median
Kuti uone huwandu hwepakati mu data rakabatanidzwa, matanho anofanirwa kutorwa ndeaya anotevera:
1. Verenga huwandu hwehuwandu (F).
2. Sarudza nzvimbo yepakati uchishandisa fomura:
\[
\text{Pakati Position} = \frac{n + 1}{2}
\]
Apo n ndiyo nhamba yedata.
3. Kuziva kirasi yepakati, kureva kirasi iri pakati.
4. Shandisa fomura yepakati yedata rakarongwa:
\[
\text{Median} = L + \left( \frac{\frac{n}{2} – F}{f} \right) \times c
\]
- L ndiyo muganho wakaderera weboka repakati.
– F inhamba inoverengwa nguva isati yasvika pachikamu chepakati.
– f ndiyo huwandu hwepakati pekirasi.
– c ndiko kureba kwechikamu chekirasi.
maitiro
Kuti uone modhi iri muboka redata, matanho anofanirwa kutorwa ndeaya:
1. Ziva kirasi yemode, kureva kirasi ine frequency yakanyanya.
2. Shandisa fomura yemode yedata rakarongwa:
\[
\text{Mode} = L + \left( \frac{d_1}{d_1 + d_2} \right) \times c
\]
- L ndiyo muganho wakaderera wekirasi yemode.
– \(d_1\) musiyano wehuwandu hwekirasi yemode nekirasi yapfuura.
– \(d_2\) musiyano wehuwandu hwema "mode class" ne "follow class".
– c ndiko kureba kwechikamu chekirasi.
Mibvunzo yemuenzaniso nekukurukurirana
Muenzaniso Mubvunzo 1: Pakati
Zvinotevera ndizvo zvinoitwa kakawanda pakuparurwa kwemhinduro dzebvunzo dzemasvomhu dzevadzidzi makumi mana:
| Kukosha | Kuwanda (f) |
|————-|——————|
| 50 – 59 | 5 |
| 60 – 69 | 10 |
| 70 – 79 | 15 |
| 80 – 89 | 7 |
| 90 – 99 | 3 |
Kuti tiverenge pakati, tinotanga taverenga nhamba yedata (n):
\[
n = 5 + 10 + 15 + 7 + 3 = 40
\]
Nzvimbo yepakati:
\[
\text{Pakati Position} = \frac{40 + 1}{2} = 20.5
\]
Tevere, tinoverenga huwandu hwehuwandu:
| Kukosha | Kuwanda (f) | Kuwanda Kwakawanda (F) |
|————-|——————|———————-|
| 50 – 59 | 5 | 5 |
| 60 – 69 | 10 | 15 |
| 70 – 79 | 15 | 30 |
| 80 – 89 | 7 | 37 |
| 90 – 99 | 3 | 40 |
Nzvimbo yepakati (20.5) iri mukirasi ye70 - 79.
Tinoshandisa fomura yepakati:
– L = 70 (muganhu wakaderera wepakati pekirasi)
– F = 15 (kuwanda kwehuwandu hwehuwandu husati hwasvika padanho repakati)
– f = 15 (huwandu hwepakati pekirasi)
– c = 10 (nguva yekirasi)
\[
\text{Median} = 70 + \left( \frac{\frac{40}{2} – 15}{15} \right) \times 10 = 70 + \left( \frac{20 – 15}{15} \right) \times 10 = 70 + \left( \frac{5}{15} \right) \times 10 = 70 + 3.33
\]
Saka, avhareji yedata iri 73.33.
Muenzaniso Mubvunzo 2: Maitiro
Zvinotevera kugoverwa kwedata pamusoro pemhedzisiro yekutengeswa kwechigadzirwa kubva muchitoro kwevhiki imwe chete:
| Huwandu hweMayuniti Akatengeswa | Kakawanda (f) |
|———————–|——————|
| 10 – 19 | 3 |
| 20 – 29 | 7 |
| 30 – 39 | 12 |
| 40 – 49 | 5 |
| 50 – 59 | 3 |
Kuti uwane modhi:
- Kirasi yemodhi ndeye 30 - 39 (frequency yepamusoro = 12).
– L = 30 (muganhu wakaderera wekirasi yemode).
– \(d_1 = 12 – 7 = 5\) (maitikiro ekirasi yemodhi – maitikiro ekirasi yapfuura).
– \(d_2 = 12 – 5 = 7\) (kazhinji kekirasi yemode – kangani kekirasi inotevera).
– c = 10 (chikamu chekirasi).
Tinoshandisa fomura yemodhi:
\[
\text{Mode} = 30 + \left( \frac{5}{5 + 7} \right) \times 10 = 30 + \left( \frac{5}{12} \right) \times 10 = 30 + 4.17 = 34.17
\]
Saka, nzira yedata iri 34.17.
Mhedziso
Kunzwisisa maverengero epakati nemodhi mudata rakabatanidzwa inyanzvi yakakosha muhuwandu hwehuwandu. Iyo median inotipa kukosha kwepakati kwedata, nepo iyo mode ichitipa kukosha kunowanzoitika kana kirasi. Nekutevera matanho uye kushandisa mafomura akatsanangurwa pamusoro, unogona kuona zviri nyore zviyero zviviri izvi zvepakati kubva padata rakabatanidzwa.
Kuburikidza nematambudziko emuenzaniso akakurukurwa, vaverengi vanotarisirwa kunzwisisa zviri nani pfungwa uye mashandisirwo e median uye mode mu data rakabatanidzwa. Kune data rakaomarara kana kugoverwa kwema frequency akareba, misimboti imwechete inogona kushandiswa nemazvo. Dzidzira matambudziko akawanda kuti usimbise kunzwisisa kwako uye hunyanzvi hwekuongorora muhuwandu.
