Imibuzo Eyisibonelo Exoxa Ngekilasi Eliphakathi Nelemodi Ledatha Yeqembu
Kuzibalo, i-median kanye ne-mode kuyizilinganiso ezimbili ezibaluleke kakhulu zokuthambekela okuphakathi. Kulesi sihloko, sizoxoxa ngezigaba ze-median kanye ne-mode ngokuningiliziwe kumongo wedatha eqoqwe ngamaqoqo, kufaka phakathi izinkinga eziningana zezibonelo ukusiza ukuqonda kwakho.
Ukuqonda i-Median kanye ne-Mode
Median
I-median yinani eliphakathi lesethi yedatha lapho idatha ihlelwa. Kumongo wedatha eqoqwe ngamaqoqo, i-median yiklasi ehlukanisa idatha ibe izingxenye ezimbili ezilinganayo.
Imodi
Imodi yinani noma ikilasi elivela kaningi kusethi yedatha. Kudatha eqoqwe ngamaqoqo, imodi yikilasi elinemvamisa ephezulu kakhulu.
Ukubala Isigaba Esimaphakathi Nesemodi Sedatha Eqoqwe
Median
Ukuze kutholakale i-median kudatha eqoqwe ngamaqembu, izinyathelo okudingeka zithathwe yilezi ezilandelayo:
1. Bala imvamisa ehlanganisiwe (F).
2. Thola indawo ephakathi nendawo usebenzisa ifomula:
\[
\umbhalo{Isikhundla Esimaphakathi} = \frac{n + 1}{2}
\]
Lapho u-n kuyinombolo yedatha.
3. Khomba isigaba esimaphakathi, okungukuthi isigaba lapho indawo ephakathi ikhona khona.
4. Sebenzisa ifomula ephakathi nendawo yedatha eqoqwe ngamaqoqo:
\[
\text{Median} = L + \left( \frac{\frac{n}{2} – F}{f} \right) \times c
\]
– L umkhawulo ophansi wesigaba esimaphakathi.
– F imvamisa ehlanganisiwe ngaphambi kwesigaba esimaphakathi.
– u-f ukuphindaphinda kwesigaba esimaphakathi.
– u-c ubude besikhawu sekilasi.
Imodi
Ukuze kunqunywe imodi kudatha eqoqwe ngamaqembu, izinyathelo okudingeka zithathwe yilezi:
1. Khomba isigaba semodi, okungukuthi isigaba esinemvamisa ephezulu kakhulu.
2. Sebenzisa ifomula yemodi yedatha eqoqwe ngamaqoqo:
\[
\text{Mode} = L + \left( \frac{d_1}{d_1 + d_2} \right) \times c
\]
– L umkhawulo ophansi wesigaba semodi.
– \(d_1\) umehluko phakathi kwemvamisa yeklasi yemodi kanye neklasi yangaphambilini.
– \(d_2\) umehluko phakathi kwemvamisa phakathi kweklasi yemodi kanye neklasi elandelayo.
– u-c ubude besikhawu sekilasi.
Imibuzo Eyisibonelo Nengxoxo
Isibonelo Umbuzo 1: Okuphakathi
Okulandelayo ukusatshalaliswa kwemiphumela yokuhlolwa kwezibalo kaningi kwabafundi abangu-40:
| Inani | Imvamisa (f) |
|————-|——————|
| 50 – 59 | 5 |
| 60 – 69 | 10 |
| 70 – 79 | 15 |
| 80 – 89 | 7 |
| 90 – 99 | 3 |
Ukuze sibale i-median, siqala ngokubala inani ledatha (n):
\[
n = 5 + 10 + 15 + 7 + 3 = 40
\]
Isikhundla esimaphakathi:
\[
\umbhalo{Isikhundla Esimaphakathi} = \frac{40 + 1}{2} = 20.5
\]
Okulandelayo, sibala imvamisa ehlanganisiwe:
| Inani | Imvamisa (f) | Imvamisa Ehlanganisiwe (F) |
|————-|——————|———————-|
| 50 – 59 | 5 | 5 |
| 60 – 69 | 10 | 15 |
| 70 – 79 | 15 | 30 |
| 80 – 89 | 7 | 37 |
| 90 – 99 | 3 | 40 |
Isikhundla esimaphakathi (20.5) sisekilasini lama-70 - 79.
Sisebenzisa ifomula ephakathi:
– L = 70 (umkhawulo ophansi wesigaba esimaphakathi)
– F = 15 (imvamisa eqongelelekayo ngaphambi kwesigaba esimaphakathi)
– f = 15 (imvamisa yekilasi eliphakathi)
– c = 10 (isikhawu sekilasi)
\[
\text{Median} = 70 + \left( \frac{\frac{40}{2} – 15}{15} \right) \times 10 = 70 + \left( \frac{20 – 15}{15} \right) \times 10 = 70 + \left( \frac{5}{15} \right) \times 10 = 70 + 3.33 = 73.33
\]
Ngakho-ke, i-median yedatha ingu-73.33.
Isibonelo Umbuzo 2: Imodi
Okulandelayo ukusatshalaliswa kwemininingwane yemiphumela yokuthengisa umkhiqizo esitolo isonto elilodwa:
| Inani lamayunithi athengisiwe | Imvamisa (f) |
|———————–|——————|
| 10 – 19 | 3 |
| 20 – 29 | 7 |
| 30 – 39 | 12 |
| 40 – 49 | 5 |
| 50 – 59 | 3 |
Ukuze uthole imodi:
– Isigaba semodi singama-30 – 39 (imvamisa ephezulu kakhulu = 12).
– L = 30 (umkhawulo ophansi wesigaba semodi).
– \(d_1 = 12 – 7 = 5\) (imodi yeklasi imvamisa – imvamisa yeklasi yangaphambilini).
– \(d_2 = 12 – 5 = 7\) (imvamisa yeklasi yemodi – imvamisa yeklasi elandelayo).
– c = 10 (isikhawu sekilasi).
Sisebenzisa ifomula yemodi:
\[
\text{Mode} = 30 + \left( \frac{5}{5 + 7} \right) \times 10 = 30 + \left( \frac{5}{12} \right) \times 10 = 30 + 4.17 = 34.17
\]
Ngakho-ke, imodi yedatha ingu-34.17.
Isiphetho
Ukuqonda ukuthi ungabala kanjani i-median kanye nemodi kudatha eqoqwe ngamaqoqo kuyikhono elibalulekile kuzibalo. I-median isinika inani eliphakathi ledatha, kuyilapho imodi isinika inani noma ikilasi elivame ukuvela. Ngokulandela izinyathelo nokusebenzisa amafomula achazwe ngenhla, ungakwazi ukunquma kalula lezi zilinganiso ezimbili zokuthambekela okuphakathi kusuka kudatha eqoqwe ngamaqoqo.
Ngezinkinga zesibonelo ezixoxwe ngazo, abafundi kulindeleke ukuthi bathole ukuqonda okungcono komqondo kanye nokusetshenziswa kwe-median kanye nemodi kudatha eqoqwe ngamaqoqo. Ukuze uthole idatha eyinkimbinkimbi kakhulu noma ukusatshalaliswa kwemvamisa ende, izimiso ezifanayo zingasetshenziswa ngokunembile. Prakthiza izinkinga eziningi ukuze uqinise ukuqonda kwakho kanye namakhono okuhlaziya kuzibalo.
