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.
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Hizi hapa alama ulizotoa: 60, 30, 45, 50, 50, 45, 40, 60, 30, 35, 40, 50, 55, 60, 30, 50, 65, 40, 50, 45, 40, 35, 50, 38, 55, 60, 40, 35, 50 Kwanza, tunapanga alama hizi kwa mpangilio wa kupanda: 30, 30, 30, 35, 35, 35, 38, 40, 40, 40, 40, 40, 45, 45, 45, 50, 50, 50, 50, 50, 50, 50, 55, 55, 60, 60, 60, 60, 65 Jumla ya alama (n) ni 29. 1. Wastani (Mean) Step 1: Jumlisha alama zote. Jumla = 30+30+30+35+35+35+38+40+40+40+40+40+45+45+45+50+50+50+50+50+50+50+55+55+60+60+60+60+65 Jumla = 1373 Step 2: Gawanya jumla ya alama kwa idadi ya alama. Wastani = JumlaIdadi ya alama = (1373)/(29) Wastani ≈ 47.34 Wastani wa alama ni 47.34. 2. Thamani ya Kati (Median) Step 1: Panga alama kwa mpangilio wa kupanda (tayari tumefanya). 30, 30, 30, 35, 35, 35, 38, 40, 40, 40, 40, 40, 45, 45, 45, 50, 50, 50, 50, 50, 50, 50, 55, 55, 60, 60, 60, 60, 65 Step 2: Tafuta thamani ya kati. Kwa kuwa kuna idadi isiyo ya kawaida ya alama (n=29), thamani ya kati ni alama ya (n+1)/(2)-th. Nafasi ya thamani ya kati = (29+1)/(2) = (30)/(2) = 15 Alama ya 15 katika orodha iliyopangwa ni 45. Thamani ya kati ya alama ni 45. 3. Njia (Mode) Step 1: Hesabu marudio ya kila alama. • 30: mara 3 • 35: mara 3 • 38: mara 1 • 40: mara 6 • 45: mara 3 • 50: mara 7 • 55: mara 2 • 60: mara 4 • 65: mara 1 Step 2: Alama inayoonekana mara nyingi zaidi ndiyo njia. Alama 50 inaonekana mara 7, ambayo ni mara nyingi zaidi kuliko alama nyingine yoyote. Njia ya alama ni 50. 3 done, 2 left today. You're making progress.