Ọnụọgụ anọ nke Data otu
Pendahuluan
Ọnụọgụgụ, ngalaba sayensị nke na-ahụ maka nchịkọta, nyocha, nkọwa, ngosipụta, na nhazi data, nwere ọtụtụ echiche dị mkpa nke na-enyere aka na mkpebi dabere na data. Otu echiche dị mkpa na nyocha data bụ quartiles. Quartiles na-enyere aka ịghọta nkesa data na otu esi ekewa data. N'isiokwu a, anyị ga-atụle quartiles n'ụzọ zuru ezu n'ihe gbasara data ejikọtara ọnụ, otu esi agbakọ ha, na otu esi akọwa nsonaazụ ya nwere ike isi nye nghọta miri emi na nkesa data.
Ịghọta Ndị Atọ
N'ikwu ya n'ụzọ dị mfe, quartile bụ ụkpụrụ ndị na-ekewa data n'ime akụkụ anọ hà nhata. N'ihe gbasara nkesa data, quartile na-ekewa data ahụ n'ime isi ihe atọ, na-emepụta oge anọ. Isi ihe atọ a: First Quartile (Q1), Second Quartile (Q2), na Third Quartile (Q3) dị mkpa maka nyocha ọnụọgụgụ. Quartile ọ bụla nwere ihe ọ pụtara na ọrụ dị iche na nghọta data ahụ.
– First Quartile (Q1): Nke a bụ uru etiti nke ọkara ala nke data ahụ, nke a makwaara dị ka pasentị nke 25.
– Nkeji nke Abụọ (Q2): Nke a bụ uru etiti nke data niile, nke a makwaara dị ka pasentị etiti ma ọ bụ pasentị iri ise.
– Atọ Quartile (Q3): Nke a bụ uru etiti nke ọkara elu nke data ahụ, nke a makwaara dị ka pasentị 75.
A na-eji quartiles akọwa akụkụ dị iche iche nke nkesa ma na-enye ozi zuru ezu gbasara oke na nkwekọ nke data ahụ.
Ọnụọgụ anọ dị na Data A chịkọtara
N'ụwa nkịtị, a naghị ejikọta data anakọtara (data raw) kama ọ bụ n'ìgwè nwere ugboro ole ha (data otu). Ịtụle data otu ezubere iche na-achọ inye ozi gbasara otu esi kesaa data ahụ n'ụdị ma ọ bụ klaasị dị iche iche. Ịgbakọ quartiles maka data otu agbakọtara gụnyere ọtụtụ usoro dị iche iche karịa maka data otu agbakọtara.
Nzọụkwụ iji gbakọọ otu ụzọ n'ụzọ anọ nke data ejikọtara ọnụ
Iji gbakọọ quartiles na data agbakọtara ọnụ, anyị chọrọ ụfọdụ ozi bụ isi site na nkesa ugboro ugboro, dị ka oke klas elu na ala, ugboro ole klaasị ọ bụla, na ugboro ole agbakọtara ọnụ. Lee usoro iji gbakọọ quartiles maka data agbakọtara ọnụ:
1. Chọpụta Klas nke Atọ:
– First Quartile (Q1): A na-ahụ ya na klaasị ebe ugboro ole a na-agbakọta na-abịaru nso \( \frac{N}{4} \)
– Nkeji nke Abụọ (Q2) ma ọ bụ Ọkara: A na-ahụ ya na klaasị ebe ugboro ole a na-agbakọta na-abịaru nso \( \frac{N}{2} \)
– Atọ Quartile (Q3): A na-ahụ ya na klaasị ebe ugboro ole a na-agbakọta na-abịaru nso \( \frac{3N}{4} \)
2. Jiri Usoro Quartile maka Data Achịkọtara:
– Usoro maka nkeji nke mbụ (Q1):
\[
Q1 = L + \left( \frac{\frac{N}{4} – Fk}{f} \right) \times c
\]
– Usoro maka nkeji nke abụọ (Q2):
\[
Q2 = L + \left( \frac{\frac{N}{2} – Fk}{f} \right) \times c
\]
– Usoro maka nkeji nke atọ (Q3):
\[
Q3 = L + \ekpe( \frac{\frac{3N}{4} – Fk}{f} \nri) \oge c
\]
Ebe:
– \( L \) bụ oke ala nke klas quartile
– \(N \) bụ mkpokọta ugboro ole
– \(Fk \) bụ ugboro mgbakọta ruo na klas quartile
– \( f \) bụ ugboro ole klas quartile dị
– \(c \) bụ obosara klas ahụ
Ihe atụ nke Ngụkọta nke Quartile maka Data Achịkọtara
Iji mee ka ọ dị mfe nghọta, ka anyị leba anya n'ihe atụ a:
Nkesa ugboro ole nke data ahụ bụ dịka ndị a:
| Oge klaasị | Ugboro ole (f) |
|———————-|——————|
| 10 – 20 | 5 |
| 20 – 30 | 8 |
| 30 – 40 | 12 |
| 40 – 50 | 7 |
| 50 – 60 | 3 |
Langkah-langkah:
1. Chọpụta N : Ngụkọta ugboro ole \( N = 5 + 8 + 12 + 7 + 3 = 35 \)
2. Ugboro Nchikota (Fk):
| Klas Oge | Ugboro (f) | Ugboro Nchikota (Fk) |
|——————-|——————————————–|
| 10 – 20 | 5 | 5 |
| 20 – 30 | 8 | 13 |
| 30 – 40 | 12 | 25 |
| 40 – 50 | 7 | 32 |
| 50 – 60 | 3 | 35 |
3. Ịchọta Klas Anọ:
– Q1: \( \frac{N}{4} = 8.75 \) dị na klas 20 - 30
– Q2: \( \frac{N}{2} = 17.5 \) dị na klas 30 - 40
– Q3: \( \frac{3N}{4} = 26.25 \) dị na klas 40 - 50
4. Ịgbakọ Kwa nkewa:
- Maka Q1:
– \( L = 20 \)
– \( Fk = 5 \)
– \( f = 8 \)
– \( c = 10 \)
\[
Q1 = 20 + \aka ekpe( \frac{8.75 – 5}{8} \aka nri) \ugboro 10 = 20 + (0.46875) \ugboro 10 = 24.6875
\]
- Maka Q2:
– \( L = 30 \)
– \( Fk = 13 \)
– \( f = 12 \)
– \( c = 10 \)
\[
Q2 = 30 + \aka ekpe( \frac{17.5 – 13}{12} \aka nri) \ugboro 10 = 30 + (0.375) \ugboro 10 = 33.75
\]
- Maka Q3:
– \( L = 40 \)
– \( Fk = 25 \)
– \( f = 7 \)
– \( c = 10 \)
\[
Q3 = 40 + \aka ekpe( \frac{26.25 – 25}{7} \aka nri) \ugboro 10 = 40 + (0.17857) \ugboro 10 = 41.7857
\]
Nkọwa nke Nsonaazụ
Site na iji mgbakọ ndị dị n'elu, anyị na-enweta nke ahụ:
– Q1 = 24.6875
– Q2 = 33.75
– Q3 = 41.7857
Ndị otu anọ a na-enye anyị ozi ndị ọzọ gbasara nkesa nke data ahụ:
– Q1=24.6875: 25% nke data dị n'okpuru 24.6875
– Q2=33.75: 50% nke data dị n'okpuru 33.75
– Q3=41.7857: 75% nke data dị n'okpuru 41.7857
Ozi nke anọ na-enyere anyị aka ịghọta mkpokọta data na ụdị mgbanwe ya. Ozi a nwere ike ịba uru nke ukwuu n'ime mkpebi na nyocha data ndị ọzọ, dịka nchọpụta ihe na-abụghị ihe dị iche ma ọ bụ nyocha arụmọrụ sistemụ.
Mmechi
Akụkụ anọ dị na data e kekọtara ọnụ na-arụ ọrụ dị oke mkpa na nyocha ọnụọgụgụ. Site na ụzọ ziri ezi, anyị nwere ike ịghọta nkesa data n'ụzọ zuru ezu na izi ezi. Ozi a abụghị naanị na-enyere aka ịkọwa data kamakwa ọ na-eme ka mkpebi dịkwuo mfe dabere na ihe akaebe e ji eme ihe. Na mmechi, ịghọta otu esi agbakọ ma kọwaa akụkụ anọ dị na data e kekọtara ọnụ bụ nkà bụ isi nke onye nyocha data ọ bụla ga-enwerịrị.
