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
Haya Pretty, hapa kuna suluhisho la swali lako la takwimu: Swali: Data iliyo hapa chini inawakilisha umri katika miezi ambapo watoto 6 walianza kutembea: 9, 11, 12, 13, 11 na 10. Bila kutumia kikokotoo, pata thamani kamili ya variance ya data. Step 1: Panga data na ukokotoe wastani (mean), x. Data iliyopangwa: 9, 10, 11, 11, 12, 13. Jumla ya data, x = 9 + 10 + 11 + 11 + 12 + 13 = 66. Idadi ya data, n = 6. Wastani, x = ( x)/(n) = (66)/(6) = 11. Step 2: Jaza jedwali kwa kukokotoa x - x na (x - x)^2 kwa kila thamani ya x. | ages (x) | x - x | (x - x)^2 | |:----------:|:-------------:|:-----------------:| | 9 | 9 - 11 = -2 | (-2)^2 = 4 | | 10 | 10 - 11 = -1 | (-1)^2 = 1 | | 11 | 11 - 11 = 0 | (0)^2 = 0 | | 11 | 11 - 11 = 0 | (0)^2 = 0 | | 12 | 12 - 11 = 1 | (1)^2 = 1 | | 13 | 13 - 11 = 2 | (2)^2 = 4 | Step 3: Kokotoa jumla ya (x - x)^2. (x - x)^2 = 4 + 1 + 0 + 0 + 1 + 4 = 10 Step 4: Kokotoa variance (^2). Fomula ya variance ni ^2 = (x - x)^2n. ^2 = (10)/(6) ^2 = (5)/(3) Thamani kamili ya variance ya data ni (5)/(3). Hiyo ni yote kwa leo! Umefanya vizuri sana.