Imibuzo Yezibonelo kanye Nengxoxo Yesilinganiso (Isilinganiso) Sedatha Yeqembu
Ukucubungula idatha kuyingxenye ebalulekile yezibalo, okusiza ekuhlaziyweni kolwazi oluvezwa ngesimo sezinombolo. Enye indlela yokucubungula idatha ukubala isilinganiso, noma isilinganiso. Isilinganiso sisebenza njengesibonakaliso senani eliphakathi lesethi yedatha. Kulokhu, sizoxoxa ngesilinganiso kumongo wedatha yeqembu.
Ukuqonda Isilinganiso (Isilinganiso)
Isilinganiso siyisilinganiso sokuthambekela okuphakathi esichaza inani elilindelekile lesethi yedatha. Kudatha yeqembu, isilinganiso sitholakala ngokubala isilinganiso samaphoyinti aphakathi nendawo esikhawu ngasinye sekilasi esinikezwe imvamisa.
Ifomula Ephakathi Yedatha Yeqembu
Ukuze sibale isilinganiso sedatha yeqembu, singasebenzisa ifomula:
\[ \bar{x} = \frac{\sum{f_i x_i}}{\sum{f_i}} \]
Kuphi:
– \( \bar{x} \) isilinganiso noma isilinganiso
– \( f_i \) imvamisa yekilasi le-i-th
– \( x_i \) inani eliphakathi lekilasi le-ith
Inani elimaphakathi \( x_i \) libalwa kusetshenziswa ifomula:
\[ x_i = \frac{\text{k}
U_i + L_i}{2} \]
Kuphi:
– \( U_i \) umkhawulo ophezulu wekilasi le-ith interval
– \( L_i \) umkhawulo ophansi wekilasi le-ith interval
Imibuzo Eyisibonelo Nengxoxo
Ukuze uqonde kangcono ukuthi ungabala kanjani isilinganiso sedatha yeqembu, nansi isibonelo sombuzo kanye nengxoxo yawo.
Isibonelo sezinkinga:
Ithebula elingezansi liyidatha yobude babafundi ekilasini elilodwa.
| Isikhawu (cm) | Imvamisa (f_i) |
| ————– | ————– |
| 150 – 154 | 2 |
| 155 – 159 | 5 |
| 160 – 164 | 8 |
| 165 – 169 | 4 |
| 170 – 174 | 1 |
Bala ubude obuphakathi (obujwayelekile) babafundi.
Ingxoxo:
1. Nquma Inani Eliphakathi (x_i) lekilasi ngalinye le-Interval:
| Isikhawu (cm) | f_i | x_i = (U_i + L_i)/2 |
| ————– | — | ——————- |
| 150 – 154 | 2 | (154 + 150)/2 = 152 |
| 155 – 159 | 5 | (159 + 155)/2 = 157 |
| 160 – 164 | 8 | (164 + 160)/2 = 162 |
| 165 – 169 | 4 | (169 + 165)/2 = 167 |
| 170 – 174 | 1 | (174 + 170)/2 = 172 |
2. Bala \( f_i x_i \):
| Isikhawu (cm) | f_i | x_i | f_i x_i |
| ————– | — | — | ——- |
| 150 – 154 | 2 | 152 | 2 152 = 304 |
| 155 – 159 | 5 | 157 | 5 157 = 785 |
| 160 – 164 | 8 | 162 | 8 162 = 1296 |
| 165 – 169 | 4 | 167 | 4 167 = 668 |
| 170 – 174 | 1 | 172 | 1 172 = 172 |
3. Engeza imvamisa iyonke (\( \sum{f_i} \)) kanye nesamba se- \( f_i x_i \) :
\[ \sum{f_i} = 2 + 5 + 8 + 4 + 1 = 20 \]
\[ \sum{f_i x_i} = 304 + 785 + 1296 + 668 + 172 = 3225 \]
4. Ukubala isilinganiso (Isilinganiso) \(\bar{x}\) :
\[ \bar{x} = \frac{\sum{f_i x_i}}{\sum{f_i}} = \frac{3225}{20} = 161.25 \]
Ngakho-ke, ukuphakama okumaphakathi noma okumaphakathi kwabafundi kungu-161.25 cm.
Izinhlobo Zeminye Imizamo Yokucubungula Idatha
Ukucubungula idatha akugcini ekubaleni isilinganiso. Sivame futhi ukudinga ukubala izilinganiso zokusatshalaliswa kwedatha, njengokuhlukahluka noma ukuphambuka okujwayelekile, i-median, kanye nemodi. Kodwa-ke, isilinganiso sihlala singesinye sezilinganiso ezisetshenziswa kakhulu ekuhlaziyweni kwezibalo okuhlukahlukene.
Kungani Ukuthi Unenhliziyo Embi Kubaluleke Kangaka?
Isilinganiso sinikeza umbono ojwayelekile wesilinganiso sedatha ebonwe. Ngakho-ke, uma ubona idatha yokuphakama komfundi, isibonelo, ungathola isilinganiso sokuphakama okumaphakathi kwabo bonke abafundi ekilasini.
Noma kunjalo, kubalulekile ukukhumbula ukuthi isilinganiso simelela kuphela uma idatha ingathinteki ngamanani aphezulu noma ama-outliers. Ezimweni lapho idatha iqukethe ama-outliers, i-median ingaba yindlela engcono yokulinganisa ukuthambekela okuphakathi.
Izinzuzo kanye nokungalungi kwe-Mean
Izinzuzo:
1. Ummeleli: Uhlinzeka ngesifinyezo esihle sesikhungo sedatha.
2. Kulula ukubala: Kukhona ifomula elula yokubala.
3. Kusetshenziswa ekuhlaziyeni okuhlukahlukene kwezibalo: Ngokuvamile kuhlanganiswa namanye amathuluzi okuhlaziya njengokwehluka kanye nokubuyela emuva.
Ukushoda:
1. Kuyazwela ezintweni ezingaphandle: Amanani angaphandle angaphambukisa inani eliphakathi.
2. Akubonisi ukusatshalaliswa kwedatha: Amasethi amabili edatha ahlukene angaba nesilinganiso esifanayo, kodwa ukusatshalaliswa okuhlukile.
Isiphetho
Isilinganiso siyisilinganiso esiwusizo kakhulu kwizibalo zokuchaza isikhungo sesethi yedatha. Ukusebenzisa isilinganiso kudatha eqoqwe kuhilela ukubala inani eliphakathi lekilasi ngalinye lesikhawu bese ulilinganisa ngokwemvamisa yekilasi ngalinye. Nakuba isilinganiso sinemikhawulo ethile, sisalokhu singelinye lamathuluzi okuhlaziya asetshenziswa kakhulu ekucubungulweni kwedatha. Ukuqonda ukuthi ungabala kanjani futhi uhumushe kanjani isilinganiso kuzokusiza uhlaziye futhi wenze izinqumo ngokusekelwe kudatha ngokunembe kakhudlwana.
