Ajụjụ Ihe Nlereanya Na-atụle Otutu nke Data A Kpọkọtara
Pendahuluan
Quartiles na ọnụ ọgụgụ bụ ihe atụ nke ọnọdụ etiti nke na-ekewa data n'ime akụkụ anọ hà nhata. Quartiles nwere quartile mbụ (Q1), quartile nke abụọ (Q2), na quartile nke atọ (Q3). N'ọtụtụ ọnọdụ, enwere ike ịchịkọta data a na-enyocha. Isiokwu a ga-atụle ihe atụ na mkparịta ụka nke quartile maka data a chịkọtara.
Ịghọta Oke na Data Otu
Quartiles bụ ụkpụrụ ndị na-ekewa data ahaziri ahazi n'ime akụkụ anọ hà nhata. A maara quartile mbụ (Q1) dị ka pasentị nke 25, a makwaara quartile nke abụọ (Q2) dị ka pasentị etiti ma ọ bụ pasentị nke 50, a makwaara quartile nke atọ (Q3) dị ka pasentị nke 75.
Maka data ejikọtara ọnụ, ịgbakọ quartiles dị ntakịrị mgbagwoju anya karịa maka otu data. A na-egosikarị data ejikọtara ọnụ na tebụl nkesa ugboro ugboro, yabụ anyị ga-eji usoro akọwapụtara iji chọta quartiles.
Usoro Quartile maka Data Achịkọtara
Iji chọta quartiles dị na data a chịkọtara, anyị na-eji usoro a:
– Nkeji mbụ (Q1):
\[
Q1 = L_{Q1} + \left( \frac{\frac{N}{4} – F_{Q1}}{f_{Q1}} \right) \times c
\]
– Nkeji nke abụọ (Q2):
\[
Q2 = L_{Q2} + \left( \frac{\frac{N}{2} – F_{Q2}}{f_{Q2}} \right) \times c
\]
– Nke atọ (Q3):
\[
Q3 = L_{Q3} + \left( \frac{\frac{3N}{4} – F_{Q3}}{f_{Q3}} \nri) \oge c
\]
Ebe:
– \( L_{Q1}, L_{Q2}, L_{Q3} \) = oke ala nke klas Q1, Q2, Q3
– \( N \) = ọnụọgụ data
– \( F_{Q1}, F_{Q2}, F_{Q3} \) = ugboro ole a na-agbakọ tupu klaasị Q1, Q2, Q3
– \( f_{Q1}, f_{Q2}, f_{Q3} \) = ugboro klaasị Q1, Q2, Q3
– \( c \) = ogologo klas
Ihe atụ nke nsogbu
Ihe na-esonụ bụ ihe atụ nke nsogbu data otu nke a ga-eji gbakọọ quartiles:
| Uru | Ugboro ole |
|————|———–|
| 10 – 19 | 5 |
| 20 – 29 | 8 |
| 30 – 39 | 12 |
| 40 – 49 | 15 |
| 50 – 59 | 6 |
| 60 – 69 | 4 |
Nzọụkwụ nke 1: Chọpụta Ugboro Nchikota
Nke mbụ, anyị kwesịrị ikpebi ugboro ole a na-agbakọ maka klaasị ọ bụla:
| Uru | Ugboro | Ugboro Nchikota |
|————|—————–|————————|
| 10 – 19 | 5 | 5 |
| 20 – 29 | 8 | 13 |
| 30 – 39 | 12 | 25 |
| 40 – 49 | 15 | 40 |
| 50 – 59 | 6 | 46 |
| 60 – 69 | 4 | 50 |
Ọnụọgụ data (N) = 50
Nzọụkwụ nke 2: Ịchọpụta Nkewa Mbụ (Q1)
– \( \ frac {N}{4} = \ frac {50}{4} = 12.5 \)
Anyị na-achọ klas ebe ugboro mkpokọta buru ụzọ gafere 12.5, ya bụ klas 20 - 29.
– L (oke dị ala nke klas Q1) = 20
– F (ugboro ole a na-agbakọ tupu klaasị Q1) = 5
– f (ugboro nke klas Q1) = 8
– c (ogologo klas) = 10
Iji usoro Q1:
\[
Q1 = 20 + \ekpe( \frac{12.5 – 5}{8} \nri) \oge 10 = 20 + \left( \frac{7.5}{8} \nri) \oge 10 = 20 + 9.375 = 29.375
\]
Nzọụkwụ nke 3: Ịchọpụta Nkeji nke Abụọ (Q2)
– \( \ frac {N}{2} = \ frac {50}{2} = 25 \)
Anyị na-achọ klas ebe ugboro mkpokọta buru ụzọ gafere 25, ya bụ klas 30 - 39.
L = 30
– F = 13
– f = 12
– c = 10
Iji usoro Q2:
\[
Q2 = 30 + \ekpe( \frac{25 – 13}{12} \nri) \oge 10 = 30 + \left( \frac{12}{12} \nri) \oge 10 = 30 + 10 = 40
\]
Nzọụkwụ nke 4: Chọpụta Nke Atọ (Q3)
– \( \frac{3N}{4} = \frac{3 \ugboro 50}{4} = 37.5 \)
Anyị na-achọ klas ebe ugboro mkpokọta buru ụzọ gafere 37.5, ya bụ klas 40 - 49.
L = 40
– F = 25
– f = 15
– c = 10
Iji usoro Q3:
\[
Q3 = 40 + \ekpe( \frac{37.5 – 25}{15} \nri) \oge 10 = 40 + \left( \frac{12.5}{15} \nri) \oge 10 = 40 + 8.333 \ihe dịka 48.333
\]
Mmechi
Site na ngụkọta ndị dị n'elu, anyị na-enweta uru nke anọ maka data otu dị ka ndị a:
– Ọnụọgụ mbụ (Q1) = 29.375
– Nkeji nke abụọ (Q2) = 40
– Ọnụọgụ atọ (Q3) = 48.333
Ụkpụrụ ndị a na-enyere anyị aka ịghọta otu esi kesaa data n'ime otu ahụ. Dịka ọmụmaatụ, 25% nke data ahụ dara n'okpuru 29.375 (Q1), 50% nke data ahụ dara n'okpuru 40 (etiti ma ọ bụ Q2), na 75% nke data ahụ dara n'okpuru 48.333 (Q3).
Ngụkọta nkewa anọ bara uru n'ọtụtụ ọnọdụ iji nweta nghọta miri emi nke nkesa data. Ịghọta usoro a na-enye anyị ohere inyocha data e kekọtara n'otu nke ọma na nke ọma.
