Nā Nīnau Laʻana a me ke Kūkākūkā ʻana o nā Heluhelu
ʻO ka helu helu kahi lālā o ka makemakika e pili ana i ka hōʻiliʻili ʻana, ka nānā ʻana, ka wehewehe ʻana, a me ka hōʻike ʻana i ka ʻikepili. Hoʻohana ʻia nā mea hana helu helu ma nā ʻano like ʻole, e like me ka hoʻokele waiwai, ka ʻenekinia, ke olakino, a me nā ʻepekema pili kanaka, e hoʻomaopopo i nā hanana i ʻike ʻia. Ma kēia ʻatikala, e kūkākūkā mākou i kekahi mau laʻana pilikia helu helu a me kā lākou wehewehe ʻana e kōkua iā ʻoe e hoʻomaopopo maikaʻi i ke kumumanaʻo.
1. Nā Waiwai ʻIkepili a me nā ʻAno Hoʻolaha
Laʻana Nīnau 1:
Ua hōʻiliʻili kekahi mea noiʻi i ka ʻikepili mai 30 mau mea pane e hoʻoholo ai i ka awelika o ka makahiki o nā kānaka ma kekahi kauhale. Ua hoʻopaʻa ʻia nā makahiki penei:
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
Ua nīnau ʻia:
1. E helu i ka awelika (awelika) o ka ʻikepili.
2. E hoʻoholo i ka waena o ka ʻikepili.
Kūkākūkā:
1. Ke helu ʻana i ka awelika:
ʻO ke ʻano awelika ka huina o nā waiwai āpau i puʻunaue ʻia e ka helu o ka ʻikepili.
ʻAwelike = (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
ʻO ke awelika = 840 / 30 = 28
No laila, ʻo ka awelika o nā makahiki o nā kānaka ma ke kauhale he 28 mau makahiki.
2. Ke hoʻoholo nei i ka Median:
ʻO ka hana mua i ka helu ʻana i ka median, ʻo ia ke hoʻokaʻawale i ka ʻikepili mai ka mea liʻiliʻi a i ka mea nui loa.
ʻIkepili i hoʻonohonoho ʻia: 22, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 32, 33, 34, 35
ʻOiai ʻo ka helu o ka ʻikepili he 30 (like), ʻo ka waena ka awelika o nā waiwai waena ʻelua.
ʻO nā waiwai awelika o ka 15 a me 16 he 29 a me 29.
Waena = (29 + 29) / 2 = 29
No laila, ʻo ka awelika o ka ʻikepili he 29 mau makahiki.
2. Ka ʻokoʻa maʻamau a me ka loli
Laʻana Nīnau 2:
Eia ka ʻikepili e pili ana i ka helu o nā malihini kipa i kēlā me kēia lā i kahi hale kūʻai i hoʻokahi pule: 120, 135, 150, 165, 180, 195, 210.
Ua nīnau ʻia:
1. E helu i ka ʻokoʻa o ka ʻikepili.
2. E helu i ka ʻokoʻa maʻamau o ka ʻikepili.
Kūkākūkā:
1. Ke helu ʻana i ka awelika:
ʻAwelike = (120 + 135 + 150 + 165 + 180 + 195 + 210) / 7 = 1155 / 7 = 165
No laila, ʻo ka awelika o nā malihini kipa i kēlā me kēia lā he 165.
2. Ke helu ʻana i ka ʻokoʻa:
ʻO ka ʻokoʻa \(\sigma^2\) ka awelika o nā huinahā o nā ʻokoʻa ma waena o kēlā me kēia ʻikepili a me ka awelika.
ʻokoʻa = \(\sum_{i=1}^{n} (x_i – \mu)^2 / n\)
ʻO \(x_i\) kēlā me kēia ʻikepili, ʻo \(\mu\) ka awelika, a ʻo n ka helu o ka ʻikepili.
\((120-165)^2 = 2025\)
\((135-165)^2 = 900\)
\((150-165)^2 = 225\)
\((165-165)^2 = 0\)
\((180-165)^2 = 225\)
\((195-165)^2 = 900\)
\((210-165)^2 = 2025\)
Huina nui = 2025 + 900 + 225 + 0 + 225 + 900 + 2025 = 6300
ʻOkoʻa = 6300 / 7 = 900
2. Ke helu ʻana i ka ʻokoʻa maʻamau:
ʻO ke ʻano maʻamau ke kumu huinaha o ka ʻokoʻa.
ʻO ke kuhi maʻamau = \(\sqrt{900}\) = 30
No laila, ʻo ka ʻokoʻa o ka ʻikepili malihini kipa i kēlā me kēia lā he 900 a ʻo ka ʻokoʻa maʻamau he 30.
3. Ka Hoʻokaʻawale Alapine (Frequency Distribution) a me ka Histogram
Laʻana Nīnau 3:
E hana i kahi papa hoʻokaʻawale alapine a me ka histogram e pili ana i ka ʻikepili e hōʻike ana i nā helu hoʻāʻo o 20 mau haumāna:
45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 60, 65, 70, 75, 80, 85, 50, 55, 60, 65
Ua nīnau ʻia:
1. E hoʻomākaukau i kahi papa hoʻokaʻawale alapine me 5 mau wā papa.
2. E hana i kahi histogram e pili ana i ka papa hoʻokaʻawale alapine.
Kūkākūkā:
1. Ke hōʻuluʻulu ʻana i kahi papa hoʻokaʻawale alapine:
ʻO 5 ka manawa papa i hoʻohana ʻia.
| Ka Wā Papa | Alapine (pinepine) |
|———————-|————–|
| 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. Ke hana ʻana i kahi Histogram:
He hōʻike kiʻi ka histogram o kahi papa hoʻolaha alapine. Hōʻike ʻia kēlā me kēia wā papa e kahi pā, a ʻo ke kiʻekiʻe o ka pā e hōʻike ana i kona alapine.
No ke kaha kiʻi ʻana, hiki iā ʻoe ke hoʻohana i nā polokalamu e like me Excel a i ʻole nā mea hana ʻike ʻikepili ʻē aʻe. Eia kahi hōʻike maʻalahi o ia ʻano histogram:
".
Ka Waena Papa: axis-x (45-49, 50-54, …, 90-94)
Alapine (frequency): y-axis
| 4
3 x
| 2 xxxxx
| 1 xxxxxxxx
|—————————————–
45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-94
".
Nānā: ʻAʻole pololei loa ka hōʻike ʻana ma o nā huapalapala ASCII. E hoʻohana i nā polokalamu kiʻi no kahi hōʻike kūpono.
Ka hopena
Ma o kēia mau nīnau hoʻohālike a me nā kūkākūkā ʻana, ua aʻo mākou pehea e helu ai i ka awelika, ka waena, ka ʻokoʻa, a me ka deviation maʻamau, a me pehea e hana ai i nā papa hoʻolaha alapine a me nā histograms mai ka ʻikepili. He mea koʻikoʻi kēia ʻike no ka nānā pono ʻana i ka ʻikepili a me ka hoʻoholo ʻana ma muli o ka ʻike helu pololei.
He mea hana ikaika ka helu helu i ka noiʻi a me nā noi kūpono. ʻO ka maikaʻi o ko kākou hoʻomaopopo ʻana i nā manaʻo kumu a me kā lākou noi, ʻo ka maikaʻi o kā kākou hoʻoponopono ʻana i nā pilikia paʻakikī a me ka hana ʻana i nā hoʻoholo naʻauao.
