This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Kusanya na Panga Data Kwanza, tunakusanya alama zote kutoka kwenye jedwali. Kuna alama 40 kwa jumla. Alama zote ni: 9.9, 6.6, 8.5, 8.7, 7.4, 10.8, 11.2, 9.1, 8.9, 12.4, 10.0, 6.4, 6.5, 7.3, 12.8, 8.2, 10.4, 8.9, 8.1, 8.8, 8.3, 9.0, 7.6, 7.1, 8.8, 11.7, 9.2, 6.2, 10.2, 9.8, 9.5, 12.3, 7.4, 7.0, 7.9, 8.6, 9.3, 6.9, 7.7, 6.2 Step 2: Unda Jedwali la Usambazaji wa Marudio (a) Tunaunda jedwali la usambazaji wa marudio kwa kutumia muda wa 1.0, kuanzia na alama ya chini kabisa ya 6.0. | Masafa ya Alama | Marudio (Frequency) | |-----------------|---------------------| | 6.0 - 6.9 | 6 | | 7.0 - 7.9 | 8 | | 8.0 - 8.9 | 10 | | 9.0 - 9.9 | 7 | | 10.0 - 10.9 | 4 | | 11.0 - 11.9 | 2 | | 12.0 - 12.9 | 3 | | Jumla | 40 | Step 3: Bainisha Alama ya Kati (Median) (b) Ili kupata alama ambayo nusu ya waombaji walipata, tunahitaji kuhesabu median. Jumla ya waombaji (N) ni 40, hivyo nusu ni (N)/(2) = (40)/(2) = 20. Tunatafuta alama ya 20 na 21. Kwanza, tunaongeza safu ya marudio jumlishi (cumulative frequency) kwenye jedwali letu: | Masafa ya Alama | Marudio (f) | Marudio Jumlishi (CF) | |-----------------|-------------|-----------------------| | 6.0 - 6.9 | 6 | 6 | | 7.0 - 7.9 | 8 | 14 | | 8.0 - 8.9 | 10 | 24 | | 9.0 - 9.9 | 7 | 31 | | 10.0 - 10.9 | 4 | 35 | | 11.0 - 11.9 | 2 | 37 | | 12.0 - 12.9 | 3 | 40 | Alama ya 20 na 21 ziko katika darasa la 8.0 - 8.9, kwa sababu marudio jumlishi hufikia 14 kabla ya darasa hili na 24 baada ya darasa hili. Hivyo, darasa la kati (median class) ni 8.0 - 8.9. Tunatumia fomula ya median kwa data iliyopangwa: Median = L + ( (N)/(2) - CFf ) × w Ambapo: L = mpaka wa chini wa darasa la kati = 8.0 N = jumla ya waombaji = 40 CF = marudio jumlishi ya darasa kabla ya darasa la kati = 14 f = marudio ya darasa la kati = 10 w = upana wa darasa = 1.0 Tunaweka namba kwenye fomula: Median = 8.0 + ( (40)/(2) - 1410 ) × 1.0 Median = 8.0 + ( (20 - 14)/(10) ) × 1.0 Median = 8.0 + ( (6)/(10) ) × 1.0 Median = 8.0 + 0.6 Median = 8.6 Alama ambayo nusu ya waombaji walipata ni 8.6. Step 4: Bainisha Idadi ya Waombaji Waliohitimu kwa Mahojiano (c) Kwa kuwa hakuna kigezo maalum cha kufuzu kilichotajwa, tunachukulia kuwa waombaji waliofuzu kwa mahojiano ya mdomo ni wale waliopata alama juu ya alama ya kati (median) tuliyoipata katika sehemu (b), yaani, alama zaidi ya 8.6. Tunatafuta alama zote ambazo ni kubwa kuliko 8.6 kutoka kwenye data asili: 9.9, 8.7, 10.8, 11.2, 9.1, 8.9, 12.4, 10.0, 12.8, 10.4, 8.9, 8.8, 9.0, 8.8, 11.7, 9.2, 10.2, 9.8, 9.5, 12.3, 9.3. Tukihesabu alama hizi, tunapata idadi ya waombaji waliofuzu. Idadi ya alama > 8.6 ni 22. Idadi ya waombaji waliofuzu kwa mahojiano ya mdomo ni 22. Tuma swali linalofuata 📸