Imibuzo Eyisibonelo Exoxa Ngesilinganiso (Isilinganiso noma Isilinganiso)
Kuzibalo, isilinganiso singenye yezindlela ezisetshenziswa kakhulu zokulinganisa ukuthambekela okuphakathi. Isilinganiso singanikeza umbono jikelele wedatha esinayo, kungaba kwezemfundo, kwezomnotho, noma kwezesayensi yezenhlalo. Lesi sihloko sizokwethula izibonelo eziningana zezinkinga ezihlobene nokubala isilinganiso kanye nengxoxo eningiliziwe yenkinga ngayinye ukuze sikusize uqonde kangcono lo mqondo.
Ukuqonda Isilinganiso (Isilinganiso)
Isilinganiso sezibalo, noma isilinganiso, yinani elitholakala ngokungeza yonke idatha bese uyihlukanisa ngenani lamaphuzu edatha. Ngokwezibalo, ifomula yesilinganiso ingabhalwa kanje:
\[ \text{Mean} = \frac{\sum x}{n} \]
Di mana:
– \( \sum x \) yisamba esiphelele sayo yonke idatha.
– \( n \) yinombolo yedatha.
Imibuzo Eyisibonelo Nengxoxo
Isibonelo Umbuzo 1
Umbuzo:
Bala isilinganiso sedatha elandelayo: 8, 10, 12, 14, 16.
Ingxoxo:
1. Hlanganisa yonke idatha:
\[ 8 + 10 + 12 + 14 + 16 = 60 \]
2. Bala inani ledatha:
\[ n = 5 \]
3. Sebenzisa ifomula ephakathi:
\[ \text{Mean} = \frac{60}{5} = 12 \]
Ngakho-ke, isilinganiso sedatha singu-12.
Isibonelo Umbuzo 2
Umbuzo:
Uma ubheka idatha yesisindo (ngama-kg) sabantu abahlanu: 55, 60, 65, 70, 75. Bala isilinganiso sesisindo.
Ingxoxo:
1. Hlanganisa isisindo somuntu ngamunye:
\[ 55 + 60 + 65 + 70 + 75 = 325 \]
2. Bala inani ledatha:
\[ n = 5 \]
3. Sebenzisa ifomula ephakathi:
\[ \text{Mean} = \frac{325}{5} = 65 \]
Ngakho-ke, isisindo esimaphakathi salezi zilwane ezinhlanu singama-65 kg.
Isibonelo Umbuzo 3
Umbuzo:
Ekilasini, amaphuzu esivivinyo sezibalo abafundi abayi-6 angama-70, 75, 65, 80, 90, kanye nama-85. Iyini incazelo yamaphuzu esivivinyo sezibalo?
Ingxoxo:
1. Hlanganisa amaphuzu okuhlolwa komfundi ngamunye:
\[ 70 + 75 + 65 + 80 + 90 + 85 = 465 \]
2. Bala inani ledatha:
\[ n = 6 \]
3. Sebenzisa ifomula ephakathi:
\[ \text{Mean} = \frac{465}{6} = 77.5 \]
Ngakho-ke, isilinganiso samaphuzu esivivinyo sezibalo ekilasini singama-77.5.
Ukusetshenziswa kwe-Mean ekuHlaziyweni kwedatha
Ukubala isilinganiso kuyisinyathelo sokuqala ekuhlaziyweni kwedatha, kodwa ukuhumusha isilinganiso kudinga umongo obanzi. Isibonelo, ezibonelweni zangaphambilini, sibale isilinganiso samaphuzu okuhlolwa, isisindo, kanye neminye idatha elula. Lezi zindlela zinikeza umqondo ojwayelekile, kodwa kunezinto eziningana ezibalulekile okufanele uzikhumbule lapho usebenzisa isilinganiso njengendlela yokulinganisa ukuthambekela okuphakathi:
1. Ukuzwela Izinto Ezingaphandle:
Izilinganiso zizwela kakhulu ezintweni ezingaphandle noma idatha eyeqile. Isibonelo, kusethi yamaphuzu okuhlolwa, umfundi oyedwa uthole u-0 kanti abanye bathole ngaphezu kuka-60. Lo 0 uzokwehlisa kakhulu isilinganiso, okwenza kube lula ukukhombisa impumelelo yangempela yeningi labafundi.
2. Isifinyezo Esiphelele:
Isilinganiso sinikeza inani elilodwa elimelela idatha, kodwa alinikezi ulwazi mayelana nokusatshalaliswa kwaleyo datha. Amasethi amabili edatha ahlukene angaba nokusatshalaliswa kwedatha okufanayo kodwa okuhlukile kakhulu.
Isibonelo Umbuzo 4 (One-Outliers)
Umbuzo:
Amaphuzu okuhlolwa kokugcina abafundi abayi-6 ami kanje: 78, 85, 82, 90, 88, kanye no-30. Bala isilinganiso samaphuzu okuhlolwa kokugcina.
Ingxoxo:
1. Isibalo samaphuzu okuhlolwa omfundi ngamunye:
\[ 78 + 85 + 82 + 90 + 88 + 30 = 453 \]
2. Bala inani ledatha:
\[ n = 6 \]
3. Sebenzisa ifomula ephakathi:
\[ \text{Mean} = \frac{453}{6} = 75.5 \]
Inani elingu-30 liphansi kakhulu futhi lithinta isilinganiso, okwenza kube ngu-75.5. Kodwa-ke, uma singazinaki izinto ezingaphandle, sithola:
\[ \text{Mean ngaphandle kuka-30} = \frac{78 + 85 + 82 + 90 + 88}{5} = \frac{423}{5} = 84.6 \]
Isilinganiso esingenazo izinto ezingaphandle siphezulu kakhulu, okubonisa ukuthi ithonya ledatha eqile libaluleke kangakanani.
Ukubala isilinganiso seqembu ledatha esetshenziswa njalo
Ngokuvamile, idatha yethulwa ngesimo sethebula lemvamisa. Ezimweni ezinjalo, kumelwe sisebenzise imvamisa njengesiphindaphindi.
Isibonelo Umbuzo 5
Umbuzo:
Njengoba kunikezwe idatha yokuphakama kweqembu labafundi:
– 150 cm kukhona abafundi abayi-5
– 155 cm kukhona abafundi abayi-8
– 160 cm kukhona abafundi abayi-7
– 165 cm kukhona abafundi abayi-10
Bala ubude obuphakathi babafundi.
Ingxoxo:
1. Phindaphinda ukuphakama ngakunye ngokuvama kwako:
\[ (150 \izikhathi 5) + (155 \izikhathi 8) + (160 \izikhathi 7) + (165 \izikhathi 10) = 750 + 1240 + 1120 + 1650 = 4760 \]
2. Inani eliphelele lama-frequency (inani labafundi):
\[ 5 + 8 + 7 + 10 = 30 \]
3. Sebenzisa ifomula ephakathi:
\[ \text{Mean} = \frac{4760}{30} \cishe kube ngu-158.67 \]
Ngakho-ke, ukuphakama okumaphakathi kwabafundi kungaba ngu-158.67 cm.
Ukuqhathaniswa kwe-Mean kanye ne-Median
Ngezinye izikhathi isilinganiso asiyona indlela engcono kakhulu yokulinganisa isikhungo sedatha, ikakhulukazi uma kukhona izinto ezingaphandle. Ezimweni ezinjalo, i-median ingaba yisinqumo esingcono. I-median iyinani eliphakathi lesethi yedatha lapho idatha ihlelwa.
Isibonelo Umbuzo 6
Umbuzo:
Bala isilinganiso kanye nesilinganiso sedatha elandelayo: 3, 5, 7, 8, 100.
Ingxoxo:
– Bala isilinganiso:
\[ \text{Mean} = \frac{3 + 5 + 7 + 8 + 100}{5} = \frac{123}{5} = 24.6 \]
– Ukuze uthole i-median, hlela idatha:
\[ 3, 5, 7, 8, 100 \]
I-median yinombolo esesikhundleni esiphakathi, okungu-7.
Lapha, i-median (7) ibonisa kangcono iningi ledatha kune-average (24.6) ethonywa yi-outlier (100).
Isiphetho
Ukubala isilinganiso kuyinto eyisisekelo kuzibalo ezisiza ekutholeni ukuqonda okujwayelekile kwesethi yedatha. Kodwa-ke, kubalulekile ukunikeza umongo kudatha nokucabangela ukusetshenziswa kwezinye izilinganiso zezibalo, njenge-median kanye nemodi, kuye ngesimo. Kubalulekile futhi ukuqaphela njalo ithonya lama-outliers lapho uhumusha isilinganiso. Ngethemba ukuthi izibonelo kanye nengxoxo engenhla kunikeze ukuqonda okucacile nokusebenzayo kokuthi ungabala kanjani futhi usebenzise kanjani isilinganiso.
