Momwe Mungadziwire Pakati kapena Avereji mu Seti ya Deta
Avereji ndi imodzi mwa njira zomwe zimagwiritsidwa ntchito kwambiri poyesa kuchuluka kwa chiwerengero cha anthu m'masamu, ziwerengero, ndi moyo watsiku ndi tsiku. Munthu akanena kuti "avereji ya kalasi" kapena "avereji ya ndalama zomwe zimagwiritsidwa ntchito pamwezi," kwenikweni amatanthauza avereji. Lingaliroli limatithandiza kumvetsetsa chithunzi chonse cha deta poika mwachidule mfundo zambiri mu nambala imodzi, yoyimira. Komabe, ngakhale zingamveke zosavuta, kudziwa avereji kumafuna njira zolondola, makamaka pamene deta ili ndi mitundu yosiyanasiyana, monga deta imodzi, deta yafupipafupi , kapena deta yogawidwa. Nkhaniyi ikufotokoza momwe mungadziwire avereji mu deta yosankhidwa bwino, ndi zitsanzo kuti zikhale zosavuta kumvetsetsa.
Kumvetsetsa Chiyerekezo (Avereji)
Avereji ndi mtengo womwe umapezeka powonjezera deta yonse kenako n’kuigawa ndi chiwerengero cha mfundo za deta. Avereji nthawi zambiri imagwiritsidwa ntchito chifukwa ndi yosavuta kuwerengera ndipo imatha kuyimira momwe deta imayendera. Mu masamu, avereji nthawi zambiri imalembedwa ndi chizindikiro \(\bar{x}\) (chotchulidwa "x bar").
Fomula yonse ya avareji ya deta imodzi ndi iyi:
\[
\bar{x} = \frac{\sum x}{n}
\]
Zambiri:
– \(\sum x\) = chiwerengero cha deta yonse
– \(n\) = kuchuluka kwa deta
Mwa kuyankhula kwina, avhareji ndi "mtengo wonse" wogawidwa ndi "chiwerengero cha mitengo".
1. Kudziwa Mean mu Deta Imodzi
Deta imodzi ndi gulu la mfundo zolembedwa momwe zilili, popanda kuikidwa m'magulu mu tebulo la ma frequency . Kuwerengera avareji pa deta imodzi n'kosavuta kwambiri.
Chitsanzo:
Zigoli za mayeso a masamu a ophunzira asanu zinali: 70, 80, 75, 85, 90.
Werengerani avareji-ake.
Gawo:
1. Onjezani mfundo zonse:
70 + 80 + 75 + 85 + 90 = 400
2. Werengani zambiri:
n = 5
3. Gawani chiwerengero cha deta ndi chiwerengero cha deta:
\(\bar{x} = 400 / 5 = 80\)
Kotero, mtengo wapakati ndi 80.
Malangizo ofunikira:
- Onetsetsani kuti deta yonse yawonjezeredwa bwino.
– Musaiwale kuwerengera kuchuluka kwa deta mosamala, makamaka ngati detayo ndi yambiri.
2. Kudziwa Avereji mu Deta ya Ma Frequency
Nthawi zina deta simawonetsedwa payokha, koma m'malo mwake ngati mtengo ndi kuchuluka kwake (kangati mtengowo umawonekera). Izi zimatchedwa deta ya pafupipafupi. Pankhaniyi, sitiwonjezera mitengoyo payokha, koma m'malo mwake timachulukitsa mtengowo ndi kuchuluka kwake.
Fomula yapakati ya deta yobwerezabwereza:
\[
\bar{x} = \frac{\sum (x \cdot f)}{\sum f}
\]
Zambiri:
– \(x\) = mtengo wa deta
– \(f\) = kuchuluka kwa kuchuluka kwa phindu
– \(\sum (x \cdot f)\) = chiwerengero cha zotsatira za kuchulukitsa mtengo ndi mafupipafupi
– \(\sum f\) = kuchuluka konse (chiwerengero chonse cha deta)
Chitsanzo:
Gome la mfundo ndi ma frequency:
| Mtengo (x) | Kuchuluka kwa nthawi (f) |
|———-:|—————–:|
| | 60 | 2 |
| | 70 | 3 |
| | 80 | 4 |
| | 90 | 1 |
Werengerani avareji.
Gawo:
1. Werengani \(x \cdot f\) pa mzere uliwonse:
– 60 × 2 = 120
– 70 × 3 = 210
– 80 × 4 = 320
– 90 × 1 = 90
2. Onjezani zotsatira:
\(\sum (x \cdot f) = 120 + 210 + 320 + 90 = 740\)
3. Onjezani ma frequency onse:
\(\sum f = 2 + 3 + 4 + 1 = 10\)
4. Gawani:
\(\bar{x} = 740 / 10 = 74\)
Kotero avareji ya deta ndi 74.
3. Kudziwa Chiŵerengero mu Deta Yogawidwa (Nthawi Yophunzirira)
Pa deta yambiri, nthawi zambiri imagawidwa m'magawo a makalasi , monga 50–59, 60–69, ndi zina zotero. Izi zimatchedwa deta yolumikizidwa. Kuti tiwerengere apakati pa deta yolumikizidwa, timagwiritsa ntchito midpoint (mtengo wapakati) wa kalasi iliyonse ngati seti yoyimira deta.
Fomula ya avareji ya deta yogawidwa m'magulu:
\[
\bar{x} = \frac{\sum (x_i \cdot f_i)}{\sum f_i}
\]
Zambiri:
– \(x_i\) = kalasi yapakati
– \(f_i\) = kuchuluka kwa kalasi
Momwe mungapezere pakati:
\[
x_i = \frac{\text{lower bound} + \text{upper bound}}{2}
\]
Chitsanzo:
Gome la deta logawidwa m'magulu:
| Nthawi | Kuchuluka (f) |
|———:|—————–:|
| 50–59 | 4 |
| 60–69 | 6 |
| 70–79 | 8 |
| 80–89 | 2 |
Gawo:
1. Dziwani pakati pa gawo lililonse:
– 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. Chulukitsani pakati ndi ma frequency:
– 54,5 × 4 = 218
– 64,5 × 6 = 387
– 74,5 × 8 = 596
– 84,5 × 2 = 169
3. Onjezani zonse:
\(\sum (x_i f_i) = 218 + 387 + 596 + 169 = 1370\)
4. Onjezani ma frequency:
\(\sum f = 4 + 6 + 8 + 2 = 20\)
5. Werengerani avareji:
\(\bar{x} = 1370 / 20 = 68,5\)
Kotero avereji ya deta yogawidwa ndi 68,5.
4. Zinthu Zofunika Kuziganizira Powerengera Pakati
Ngakhale kuti njira yapakati imawoneka yosavuta, pali zinthu zingapo zofunika kuti zitsimikizire zotsatira zolondola za kuwerengera:
1. Avereji imakhudzidwa ndi zinthu zopitirira muyeso
Ngati pali zinthu zazikulu kwambiri kapena zazing'ono kwambiri (zopanda phindu), avareji imatha kusintha kwambiri. Mwachitsanzo, ndalama zapakati zidzakwera ngati munthu m'modzi ali ndi ndalama zambiri.
2. Onetsetsani kuti mtundu wa deta ndi wolondola
Avereji ndi yoyenera pa deta ya manambala (manambala). Pa deta yamagulu monga "mtundu womwe mumakonda" kapena "mtundu wa galimoto," avereji singagwiritsidwe ntchito.
3. Gwiritsani ntchito kuzungulira ngati pakufunika
Mu deta yolumikizidwa m'magulu, apakati nthawi zambiri amakhala decimal. Dulani apakati ngati pakufunika (monga, m'malo awiri a decimal).
4. Yang'ananinso kuchuluka kwa nthawi yonse
Mu deta ya ma frequency kapena magulu, cholakwika chofala ndi kuwonjezera ma frequency molakwika, zomwe zimapangitsa kuti pakhale kugawa kolakwika.
5. Kugwiritsa Ntchito Mean mu Moyo wa Tsiku ndi Tsiku
Mean siigwiritsidwa ntchito m'makalasi a masamu okha, komanso m'magawo osiyanasiyana:
- Maphunziro: kudziwa zigoli zapakati pa mayeso a ophunzira.
– Zachuma: kuwerengera ndalama zomwe amapeza, mtengo wapakati wa katundu.
– Thanzi: kuthamanga kwa magazi kwapakati, kudya ma calories apakati.
– Masewera: mapointi apakati pa masewera.
- Bizinesi: malonda apakati a tsiku lililonse kapena pamwezi.
Mwa kumvetsetsa avareji, titha kupanga zisankho kutengera deta mwanjira yomveka bwino komanso yoyezeka.
Mapeto
Kudziwa avareji kapena avareji ya seti ya deta kungathe kuchitika m'njira zingapo, kutengera mtundu wa deta. Pa seti imodzi ya deta, avareji imapezeka pogawa chiwerengero cha seti ya deta ndi chiwerengero cha seti ya deta. Pa seti ya deta ya mafupipafupi, chiwerengero cha mitengo yochulukitsidwa ndi mafupipafupi awo chimagawidwa ndi mafupipafupi onse. Pa seti ya deta yogawidwa m'magulu, avareji imawerengedwa pogwiritsa ntchito pakati pa gawo lililonse la kalasi ngati seti yoyimira deta. Potsatira njira zolondola komanso zolondola, avareji ikhoza kukhala chida chothandiza kwambiri pakumvetsetsa ndi kusanthula deta m'mikhalidwe yosiyanasiyana.
Ngati mukufuna, nditha kupanganso "kalembedwe ka blog" (komasuka kwambiri) ka nkhaniyi, kapena kuwonjezera mafunso ndi mayankho kuti zikhale zosavuta kumvetsetsa.
