Misalin Tambayoyi Game da Kashi na Bayanan Rukuni
Kashi ɗaya ma'auni ne na matsayi a cikin kididdigar da ake amfani da ita don fahimtar rarraba bayanai. A cikin wannan labarin, za mu tattauna dalla-dalla yadda ake tantance kashi ɗaya don bayanan da aka haɗa. Za mu haɗa da misalai da yawa da bayaninsu don fayyace wannan ra'ayi. Bari mu fara da fahimtar asali game da kashi ɗaya sannan mu ci gaba zuwa ga misalan da bayaninsu.
Fahimtar Kashi
Kashi ɗaya (percentile) ƙima ce da ke raba bayanai zuwa sassa 100 daidai. Wato, kashi ɗaya (nth percentile) ita ce ƙimar da ke ƙasa wadda kashi ɗaya (n%) na bayanan da ke cikin rarrabawa suka faɗi. Misali, idan bayanan suna da kashi ɗaya (25%) na bayanai (P25), hakan yana nufin kashi ɗaya (25%) na bayanai sun faɗi ƙasa da wannan ƙima.
A cikin bayanan da aka haɗa a rukuni, sau da yawa muna amfani da teburin rarraba mita don tsara bayanan sannan mu tantance kashi-kashi masu dacewa. Waɗannan tebura suna gabatar da bayanai a cikin takamaiman tazara azuzuwan, suna ba mu damar fahimtar rarraba bayanai dalla-dalla.
Tsarin Kashi a cikin Bayanan Rukuni
Tsarin da aka tsara don tantance kashi na n (Pn) a cikin bayanan rukuni shine kamar haka:
\[
P_n = L + \left( \frac{nN – \sum f_{\text{before}}}{f_{k}} \right) \times c
\]
Ina:
– \(P_n\) shine kashi na nth.
– \(L\) shine ƙananan gefen tazara na ajin kashi-kashi.
– \(n\) shine kashi da ake so (misali, ga P25, n = 25).
– \(N\) shine jimlar adadin mitoci masu tarawa.
– \(\sum f_{\text{before}}\) shine yawan tarawa kafin tazara ajin kashi-kashi.
– \(f_{k}\) shine mitar tazara ajin kashi-kashi.
– \(c\) shine tsawon tazara ajin.
Misalin matsalolin
Domin mu fahimci sosai, bari mu duba tambayar da ke tafe mu tattauna ta dalla-dalla.
Misali Tambaya ta 1
A wani bincike, an samu bayanai game da tsayin (a cikin cm) na ɗaliban makarantar sakandare 100 na aji 10 kamar haka:
| Tazarar Aji | Mita |
|——————-|———–|
| 150 – 154 | 5 |
| 155 – 159 | 8 |
| 160 – 164 | 12 |
| 165 – 169 | 20 |
| 170 – 174 | 30 |
| 175 – 179 | 15 |
| 180 – 184 | 10 |
Lissafa kashi 40 cikin ɗari (P40) na bayanan.
Matakai don Warwarewa
1. Ƙayyade yawan tarawa ga kowane aji:
| Tazarar Aji | Mita | Mita Tarawa |
|——————-|—————–|—————————|
| 150 – 154 | 5 | 5 |
| 155 – 159 | 8 | 13 |
| 160 – 164 | 12 | 25 |
| 165 – 169 | 20 | 45 |
| 170 – 174 | 30 | 75 |
| 175 – 179 | 15 | 90 |
| 180 – 184 | 10 | 100 |
2. Gano tazarar kashi-kashi na aji (P40):
Tunda muna neman P40, muna buƙatar kashi 40% na ɗalibai 100, wato ɗalibai 40. Idan muka duba teburin mitar da aka tara, mun ga cewa ɗalibai 40 suna kwance a tazara tsakanin 165 - 169 cm saboda 45 shine mitar da aka tara ta farko da ta wuce 40.
3. Nemo dabi'un da ake buƙata a cikin dabarar:
– \(L = 164.5\)
– \(nN = 40\)
– \(\sum f_{\text{kafin}} = 25\)
– \(f_k = 20\)
– \(c = 5\)
4. Shigar da dabi'u a cikin dabarar:
\[
P_{40} = 164.5 + \left( \frac{40 – 25}{20} \right) \times 5
\]
\[
P_{40} = 164.5 + \left( \frac{15}{20} \right) \times 5
\]
\[
P_{40} = 164.5 + 0.75 \sau 5
\]
\[
P_{40} = 164.5 + 3.75
\]
\[
P_{40} = 168.25
\]
Don haka, kashi 40 cikin ɗari (P40) na bayanan shine 168.25 cm.
Misali Tambaya ta 2
A ce akwai bayanan maki na jarrabawar lissafi daga ƙungiyar ɗalibai 200:
| Tazarar Aji | Mita |
|——————-|———–|
| 40 – 44 | 10 |
| 45 – 49 | 18 |
| 50 – 54 | 32 |
| 55 – 59 | 45 |
| 60 – 64 | 50 |
| 65 – 69 | 25 |
| 70 – 74 | 12 |
| 75 – 79 | 8 |
Lissafa kashi 75 cikin ɗari (P75) na bayanan.
Matakai don Warwarewa
1. Ƙayyade yawan tarawa ga kowane aji:
| Tazarar Aji | Mita | Mita Tarawa |
|——————-|—————–|—————————|
| 40 – 44 | 10 | 10 |
| 45 – 49 | 18 | 28 |
| 50 – 54 | 32 | 60 |
| 55 – 59 | 45 | 105 |
| 60 – 64 | 50 | 155 |
| 65 – 69 | 25 | 180 |
| 70 – 74 | 12 | 192 |
| 75 – 79 | 8 | 200 |
2. Gano tazarar kashi-kashi na aji (P75):
Tunda muna neman P75, muna buƙatar kashi 75% na ɗalibai 200, wato ɗalibai 150. Idan muka duba yawan adadin da ake buƙata, za mu ga cewa ɗalibai 150 suna faɗuwa a tazara tsakanin 60 zuwa 64 a aji.
3. Nemo ƙimar da ake buƙata:
– \(L = 59.5\)
– \(nN = 150\)
– \(\sum f_{\text{kafin}} = 105\)
– \(f_k = 50\)
– \(c = 5\)
4. Shigar da dabi'u a cikin dabarar:
\[
P_{75} = 59.5 + \left( \frac{150 – 105}{50} \right) \times 5
\]
\[
P_{75} = 59.5 + \left( \frac{45}{50} \right) \times 5
\]
\[
P_{75} = 59.5 + 0.9 \sau 5
\]
\[
P_{75} = 59.5 + 4.5
\]
\[
P_{75} = 64
\]
Don haka, kashi 75 cikin ɗari (P75) na bayanan shine 64.
Kammalawa
A cikin wannan labarin, mun tattauna yadda ake tantance kashi-kashi na bayanai da aka haɗa ta amfani da dabarun lissafi da kuma wasu misalai da dama. Kashi-kashi kayan aiki ne mai amfani a cikin kididdiga don fahimtar rarraba bayanai da kuma tantance matsayin da ke tsakanin ƙimar bayanai. Ta hanyar fahimtar yadda ake ƙididdige kashi-kashi a cikin bayanan da aka haɗa, za mu iya yin nazarin bayanan sosai. Muna fatan waɗannan matsalolin misalai da tattaunawa sun taimaka muku fahimtar manufar kashi-kashi a cikin bayanan da aka haɗa.
