Tambayoyi da Tattaunawa kan Matakan Rarrabawa
Ma'aunin wargajewa ra'ayoyi ne na ƙididdiga da ake amfani da su don bayyana yadda aka rarraba ko aka bambanta bayanai a cikin saitin bayanai. Girman wargajewa yana ba da zurfin nazari kan rarraba bayanai, yana bayyana bayanan da ba za a iya gani kawai daga matsakaici da matsakaici ba. Wannan labarin zai tattauna misalai da yawa na matsaloli da suka shafi ma'aunin wargajewa da tattaunawarsu don fayyace wannan ra'ayi. Akwai ma'auni daban-daban na wargajewa, gami da kewayon, karkacewar daidaito, bambancin, da kewayon interquartile (IQR).
1. Nisa
Tabbas
Zangon shine bambanci tsakanin mafi girma da mafi ƙanƙanta dabi'u a cikin saitin bayanai.
Misalin matsalolin
Wata ƙungiyar ƙwallon ƙafa ta rubuta adadin kwallayen da ta zura a wasanni 10 da suka gabata kamar haka:
3, 5, 2, 8, 7, 2, 6, 9, 4, da 1.
Tattaunawa
Don ƙididdige kewayon, muna buƙatar nemo matsakaicin da ƙimar mafi ƙarancin bayanai.
– Matsakaicin maki: 9
– Mafi ƙarancin ƙima: 1
Kewaya = Matsakaicin ƙima – Mafi ƙarancin ƙima = 9 – 1 = 8
Don haka, yawan kwallayen da aka zura a wasanni 10 da suka gabata shine kwallaye 8.
2. Daidaitaccen Canji
Tabbas
Bambancin daidaito shine ma'auni na nisan kowace ƙima a cikin tarin bayanai daga matsakaicinsa. Bambancin daidaito shine tushen murabba'in bambancin.
Misalin matsalolin
Ga sakamakon jarabawar lissafi na aji: 65, 70, 75, 80, da 85.
Tattaunawa
Mataki na farko shine a ƙididdige matsakaicin maki.
\[
\text{Matsakaici} = \frac{65 + 70 + 75 + 80 + 85}{5} = 75
\]
Mataki na biyu shine a ƙididdige bambanci tsakanin kowace ƙima da matsakaici, sannan a yi murabba'i a sakamakon:
– (65 – 75)² = 100
– (70 – 75)² = 25
– (75 – 75)² = 0
– (80 – 75)² = 25
– (85 – 75)² = 100
Mataki na uku shine a nemo bambancin ta hanyar ƙididdige matsakaicin murabba'in bambance-bambancen:
\[
\text{Bambanci} = \frac{100 + 25 + 0 + 25 + 100}{5} = 50
\]
Bambancin da aka saba dashi shine tushen murabba'in bambancin:
\[
\text{Bambancin yau da kullun} = \sqrt{50} \approx 7.07
\]
Don haka daidaitaccen karkacewar sakamakon gwaji shine kusan 7.07.
3. Bambanci
Tabbas
Bambanci shine matsakaicin bambance-bambancen murabba'i tsakanin kowace ƙima da matsakaicinta; yana bayyana yadda aka rarraba bayanai a kusa da matsakaicin. Bambanci shine murabba'in karkacewar da aka saba.
Misalin matsalolin
A ce muna da waɗannan bayanai: 10, 20, 30, 40, da 50.
Tattaunawa
Mataki na farko shine a ƙididdige matsakaicin bayanan.
\[
\text{Matsakaici} = \frac{10 + 20 + 30 + 40 + 50}{5} = 30
\]
Mataki na biyu shine a ƙididdige bambanci tsakanin kowace ƙima da matsakaici, sannan a yi murabba'i a sakamakon:
– (10 – 30)² = 400
– (20 – 30)² = 100
– (30 – 30)² = 0
– (40 – 30)² = 100
– (50 – 30)² = 400
Mataki na uku shine a nemo bambancin ta hanyar ƙididdige matsakaicin murabba'in bambance-bambancen:
\[
\text{Bambanci} = \frac{400 + 100 + 0 + 100 + 400}{5} = 200
\]
Saboda haka, bambancin bayanai shine 200.
4. Tsakanin Tsakanin Yankuna (IQR)
Tabbas
Tsarin interquartile (IQR) shine bambanci tsakanin kwata na uku (Q3) da kwata na farko (Q1). IQR yana ba da ma'aunin yaduwa daga tsakiyar kashi 50% na bayanan da ke cikin tarin bayanai, wanda zai iya zama mai ba da labari fiye da kewayon.
Misalin matsalolin
Bayanan da ke ƙasa suna da ƙimomin: 1, 3, 4, 5, 6, 7, 8, 11, 13, da 14.
Tattaunawa
Da farko, dole ne mu tsara bayanai:
1, 3, 4, 5, 6, 7, 8, 11, 13, 14
Don ƙididdige Q1 da Q3, muna buƙatar raba bayanan zuwa kwata-kwata.
– Matsakaicin (Q2) yana tsakanin 6 da 7: \((6+7)/2 = 6.5\)
Ga Q1, mun ɗauki matsakaicin ƙimar da ke ƙasa:
– 1, 3, 4, 5, 6
– Matsakaicin wannan rukunin shine 4
Don Q3, mun ɗauki matsakaicin ƙimar sama:
– 7, 8, 11, 13, 14
– Matsakaicin wannan rukunin shine 11
Matsakaicin Range (IQR) = Q3 – Q1 = 11 – 4 = 7
Saboda haka, IQR na bayanan shine 7.
Kammalawa
Ma'aunin wargajewa muhimman fannoni ne na kididdiga waɗanda ke taimaka mana mu fahimci matakin bambancin bayanai. A cikin wannan labarin, mun tattauna kuma mun bayar da misalai da tattaunawa kan ma'auni da yawa da ake amfani da su na wargajewa: kewayon, karkacewar daidaito, bambancin ra'ayi, da kewayon interquartile. Ta hanyar fahimtar waɗannan ra'ayoyi da yadda ake ƙididdige su, muna samun fahimtar halayen bayanan da muke nazari a kansu, wanda hakan zai iya taimaka mana mu yanke shawara mai zurfi bisa ga waɗannan bayanan.
