Tambayoyi da Tattaunawa game da Ƙididdiga
Kididdiga wani reshe ne na lissafi wanda ya shafi tattarawa, nazari, fassara, da gabatar da bayanai. Ana amfani da kayan aikin kididdiga a fannoni daban-daban, kamar tattalin arziki, injiniyanci, lafiya, da kimiyyar zamantakewa, don fahimtar abubuwan da aka lura. A cikin wannan labarin, za mu tattauna misalan matsalolin kididdiga da dama da kuma bayaninsu don taimaka muku fahimtar ra'ayin sosai.
1. Halayen Bayanai da Nau'in Rarrabawa
Misali Tambaya ta 1:
Wani mai bincike ya tattara bayanai daga mutane 30 da aka yi wa tambayoyi domin tantance matsakaicin shekarun mutane a wani ƙauye. An rubuta waɗannan shekarun:
25, 30, 22, 28, 34, 29, 31, 24, 26, 27 29 30 31 33 35 24 26 28 29 27 30 32 26 25 28 31 29 30 24 32 XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX, XNUMX, XNUMX, XNUMX, XNUMX
An tambaya:
1. Lissafa matsakaicin (matsakaici) na bayanan.
2. Ka tantance matsakaicin bayanan.
Tattaunawa:
1. Lissafin Ma'aunin:
Ma'anar ita ce jimlar dukkan dabi'u da aka raba da adadin bayanai.
Matsakaici = (25 + 30 + 22 + 28 + 34 + 29 + 31 + 24 + 26 + 27 + 29 + 30 + 31 + 33 + 35 + 24 + 26 + 28 + 29 + 27 + 30 + 32 + 26 + 25 + 28 + 31 + 29 + 30 + 24 + 32) / 30
Matsakaicin = 840 / 30 = 28
Don haka, matsakaicin shekarun mutanen ƙauyen shine shekaru 28.
2. Ƙayyade Matsakaici:
Mataki na farko wajen ƙididdige matsakaicin bayanai shine a rarraba bayanai daga ƙarami zuwa babba.
Bayanan da aka tsara: 22, 24, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 31, 31, 31, 32, 32, 33, 34, 35
Tunda adadin bayanai 30 ne (kowanne), matsakaicin shine matsakaicin ƙimar tsakiya guda biyu.
Matsakaicin ƙimar 15 da 16 sune 29 da 29.
Matsakaici = (29 + 29) / 2 = 29
Don haka, matsakaicin bayanin shine shekaru 29.
2. Bambancin Daidaitacce da Bambancin
Misali Tambaya ta 2:
Ga bayanai kan adadin masu ziyartar shago a kowace rana a cikin mako guda: 120, 135, 150, 165, 180, 195, 210.
An tambaya:
1. Lissafa bambancin bayanai.
2. Lissafa karkacewar da aka saba yi na bayanai.
Tattaunawa:
1. Lissafin Ma'aunin:
Matsakaici = (120 + 135 + 150 + 165 + 180 + 195 + 210) / 7 = 1155 / 7 = 165
Don haka, matsakaicin masu ziyara a kowace rana shine 165.
2. Lissafin Bambancin:
Bambancin \(\sigma^2\) shine matsakaicin murabba'in bambance-bambancen da ke tsakanin kowace bayanai da matsakaicin.
Bambancin = (\sum_{i=1}^{n} (x_i – \mu)^2 / n\)
Inda \(x_i\) yake kowanne bayanai, \(\mu\) shine matsakaicin, kuma n shine adadin bayanai.
\((120-165)^2 = 2025\)
\((135-165)^2 = 900\)
\((150-165)^2 = 225\)
\((165-165)^2 = 0\)
\((180-165)^2 = 225\)
\((195-165)^2 = 900\)
\((210-165)^2 = 2025\)
Jimlar jimilla = 2025 + 900 + 225 + 0 + 225 + 900 + 2025 = 6300
Bambancin = 6300 / 7 = 900
2. Lissafin Daidaitaccen Bambanci:
Bambancin da aka saba dashi shine tushen murabba'in bambancin.
Bambancin da aka saba = \(\sqrt{900}\) = 30
Don haka, bambancin bayanan masu ziyara na yau da kullun shine 900 kuma daidaitaccen karkacewar shine 30.
3. Rarraba Mita da Histogram
Misali Tambaya ta 3:
Ƙirƙiri teburin rarraba mita da histogram bisa ga bayanan da ke ƙasa waɗanda ke nuna sakamakon jarrabawa na ɗalibai 20:
45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 60, 65, 70, 75, 80, 85, 50, 55, 60, 65
An tambaya:
1. Shirya teburin rarraba mita tare da tazara tsakanin aji 5.
2. Ƙirƙiri histogram bisa ga teburin rarraba mitar.
Tattaunawa:
1. Tattara Teburin Rarraba Mita:
Tazarar da aka yi amfani da ita a aji ita ce 5.
| Tazarar Aji | Mita |
|——————-|———–|
| 45 – 49 | 1 |
| 50 – 54 | 2 |
| 55 – 59 | 2 |
| 60 – 64 | 4 |
| 65 – 69 | 3 |
| 70 – 74 | 2 |
| 75 – 79 | 2 |
| 80 – 84 | 2 |
| 85 – 89 | 2 |
| 90 – 94 | 1 |
2. Ƙirƙirar Histogram:
Histogram misali ne na zane na teburin rarraba mita. Kowane tazara ajin yana wakiltar sandar, kuma tsayin sandar yana nuna mitar sa.
Don tsara shi, zaku iya amfani da software kamar Excel ko wasu kayan aikin hangen nesa na bayanai. Ga misali mai sauƙi na irin wannan histogram:
““
Tazarar Aji: x-axis (45-49, 50-54, …, 90-94)
Mita: y-axis
| 4
| 3 x
| 2 xxxxx
| 1 xxxxxxxxx
|——————————————–
45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-94
““
Lura: Wakiltar ta hanyar haruffan ASCII ba ta da cikakken daidaito. Yi amfani da manhajar zane-zane don wakilcin da ya fi dacewa.
Kammalawa
Ta hanyar waɗannan tambayoyi da tattaunawa na misali, mun koyi yadda ake ƙididdige matsakaicin, matsakaici, bambancin, da karkacewar daidaito, da kuma yadda ake ƙirƙirar tebura da histograms na rarraba mita daga bayanai. Wannan fahimtar tana da mahimmanci don yin nazarin bayanai yadda ya kamata da kuma yanke shawara bisa ga ingantaccen bayanin kididdiga.
Kididdiga kayan aiki ne mai ƙarfi a bincike da aikace-aikace na zahiri. Da zarar mun fahimci muhimman ra'ayoyi da aikace-aikacensu, da kyau za mu iya magance matsaloli masu sarkakiya da kuma yanke shawara mai ma'ana.
