Rubu'i na Bayanan Rukuni
Pendahuluan
Kididdiga, wani reshe na kimiyya da ke magana kan tattarawa, nazari, fassara, gabatarwa, da kuma tsara bayanai, yana da muhimman ra'ayoyi da yawa waɗanda ke taimakawa wajen yanke shawara bisa ga bayanai. Wani muhimmin ra'ayi na kididdiga a cikin nazarin bayanai shine quartiles. Quartiles yana taimakawa wajen fahimtar rarraba bayanai da kuma yadda ake rarraba bayanai. A cikin wannan labarin, za mu tattauna quartiles dalla-dalla a cikin mahallin bayanan da aka haɗa, yadda ake ƙididdige su, da kuma yadda fassarar sakamakon zai iya samar da zurfafa fahimta game da rarraba bayanai.
Fahimtar Ƙidaya
A taƙaice dai, kwata-kwata dabi'u ne da ke raba bayanai zuwa sassa huɗu daidai. A cikin mahallin rarraba bayanai, kwata-kwata suna raba bayanai zuwa maki uku, suna samar da tazara huɗu. Waɗannan maki uku: Kwata-kwata na Farko (Q1), Kwata-kwata na Biyu (Q2), da Kwata-kwata na Uku (Q3) suna da mahimmanci ga nazarin ƙididdiga. Kowane kwata-kwata yana da ma'ana da aiki daban-daban wajen fahimtar bayanan.
– Rukunin Farko (Q1): Wannan shine matsakaicin ƙimar rabin ƙasa na bayanan, wanda aka fi sani da kashi 25 cikin ɗari.
– Kwata na Biyu (Q2): Wannan shine matsakaicin ƙimar duk bayanan, wanda kuma aka sani da matsakaicin kashi ko kashi 50.
– Kwata na Uku (Q3): Wannan shine matsakaicin ƙimar rabin saman bayanai, wanda aka fi sani da kashi 75 cikin ɗari.
Ana amfani da quartiles don bayyana fannoni daban-daban na rarrabawa da kuma samar da ƙarin bayani game da iyaka da daidaiton bayanan.
Rukuni a cikin Bayanan Rukuni
A zahirin duniya, bayanai da aka tattara ba a haɗa su cikin rukuni-rukuni ba (bayanan da ba a haɗa su ba) sai dai a cikin rukuni-rukuni masu mitar su (bayanan da aka haɗa su). Binciken bayanan da aka haɗa cikin rukuni yana nufin samar da bayanai game da yadda ake rarraba bayanan a cikin rukunoni ko azuzuwa daban-daban. Lissafin kwata-kwata don bayanan da aka haɗa cikin rukuni ya ƙunshi matakai daban-daban fiye da na bayanan da ba a haɗa su cikin rukuni ba.
Matakai don Lissafin Kwata-kwata na Bayanan Rukuni
Domin ƙididdige kwata-kwata a cikin bayanan da aka haɗa, muna buƙatar wasu bayanai na asali daga rarrabawar mita, kamar iyakokin aji na sama da na ƙasa, mitar kowane aji, da kuma mitar da aka haɗa. Ga matakan ƙididdige kwata-kwata don bayanan da aka haɗa:
1. Kayyade Ajin Kwata-kwata:
– Rukunin Farko (Q1): Ana samunsa a cikin azuzuwan da mitar tarin ta kusanci \( \frac{N}{4} \)
– Kwata na Biyu (Q2) ko Tsakiya: Ana samunsa a cikin azuzuwan da mitar tarin ta kusanci \( \frac{N}{2} \)
– Rukunin Uku (Q3): Ana samunsa a cikin azuzuwan da mitar tarin ta kusanci \( \frac{3N}{4} \)
2. Yi amfani da Tsarin Rukunin Ma'auni don Bayanan Rukuni:
– Tsarin Kwata na Farko (Q1):
\[
Q1 = L + \left( \frac{\frac{N}{4} – Fk}{f} \right) \times c
\]
– Tsarin Kwata na Biyu (Q2):
\[
Q2 = L + \left( \frac{\frac{N}{2} – Fk}{f} \right) \times c
\]
– Tsarin Kwata na Uku (Q3):
\[
Q3 = L + \left( \frac{\frac{3N}{4} – Fk}{f} \right) \times c
\]
Ina:
– \( L \) shine ƙananan iyaka na ajin kwata
– \( N \) shine jimlar mitar
– \( Fk \) shine yawan tarawa har zuwa aji na kwata
– \( f \) shine mitar ajin kwata
– \( c \) shine faɗin aji
Misali na Lissafin Kwata-kwata don Bayanan Rukuni
Domin fahimtarsa cikin sauƙi, bari mu dubi misali mai zuwa:
Rarraba mitar bayanai kamar haka:
| Tazarar Aji | Mita (f) |
|——————-|———————|
| 10 – 20 | 5 |
| 20 – 30 | 8 |
| 30 – 40 | 12 |
| 40 – 50 | 7 |
| 50 – 60 | 3 |
Matakai:
1. Kayyade N : Jimlar mita \( N = 5 + 8 + 12 + 7 + 3 = 35 \)
2. Mitar Tarawa (Fk):
| Ajin Tazara | Mita (f) | Mita Tarawa (Fk) |
|——————-|————————|—————————–|
| 10 – 20 | 5 | 5 |
| 20 – 30 | 8 | 13 |
| 30 – 40 | 12 | 25 |
| 40 – 50 | 7 | 32 |
| 50 – 60 | 3 | 35 |
3. Nemo Azuzuwan Kwata-kwata:
– Q1: \( \frac{N}{4} = 8.75 \) yana cikin aji 20 - 30
– Q2: \( \frac{N}{2} = 17.5 \) yana cikin aji 30 - 40
– Q3: \( \frac{3N}{4} = 26.25 \) yana cikin aji 40 - 50
4. Lissafin Kwata-kwata:
– Don Q1:
– \( L = 20 \)
– \( Fk = 5 \)
– \( f = 8 \)
– \( c = 10 \)
\[
Q1 = 20 + \left( \frac{8.75 – 5}{8} \right) \times 10 = 20 + (0.46875) \times 10 = 24.6875
\]
– Don Q2:
– \( L = 30 \)
– \( Fk = 13 \)
– \( f = 12 \)
– \( c = 10 \)
\[
Q2 = 30 + \left( \frac{17.5 – 13}{12} \right) \times 10 = 30 + (0.375) \times 10 = 33.75
\]
– Don Q3:
– \( L = 40 \)
– \( Fk = 25 \)
– \( f = 7 \)
– \( c = 10 \)
\[
Q3 = 40 + \left( \frac{26.25 – 25}{7} \right) \times 10 = 40 + (0.17857) \times 10 = 41.7857
\]
Fassarar Sakamako
Ta amfani da lissafin da ke sama, mun sami cewa:
– Q1 = 24.6875
– Q2 = 33.75
– Q3 = 41.7857
Waɗannan kwata-kwata suna ba mu ƙarin bayani game da rarraba bayanan:
– Q1=24.6875: 25% na bayanai suna ƙasa da 24.6875
– Q2=33.75: 50% na bayanai suna ƙasa da 33.75
– Q3=41.7857: 75% na bayanai suna ƙasa da 41.7857
Bayani mai sassa huɗu yana ba mu damar fahimtar yawan bayanai da kuma bambancinsu. Wannan bayanin zai iya zama da amfani sosai wajen yanke shawara da kuma ƙarin nazarin bayanai, kamar gano abubuwan da ba su dace ba ko kimanta aikin tsarin.
Kammalawa
Rubu'i-rubu'i a cikin bayanan da aka haɗa suna taka muhimmiyar rawa a cikin nazarin ƙididdiga. Da hanyoyin da suka dace, za mu iya fahimtar rarraba bayanai dalla-dalla da daidaito. Wannan bayanin ba wai kawai yana taimakawa fassarar bayanai ba ne, har ma yana sauƙaƙa yanke shawara mai zurfi bisa ga shaidar gwaji. A ƙarshe, fahimtar yadda ake ƙididdigewa da fassara rubu'i-rubu'i a cikin bayanan da aka haɗa ƙungiya wata muhimmiyar fasaha ce da kowane mai nazarin bayanai dole ne ya ƙware.
