Marks: 60, 30, 45, 50, 50, 45, 40, 60, 30, 35, 40, 50, 55, 60, 30, 50, 65, 42, 50, 45, 40, 35, 50, 30, 38…

Question

Marks: 60, 30, 45, 50, 50, 45, 40, 60, 30, 35, 40, 50, 55, 60, 30, 50, 65, 42, 50, 45, 40, 35, 50, 30, 38, 55, 60, 40, 35, 50

ScanSolve AI Tutor · Accepted Answer

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)

Jumlisha alama zote.
$\text{Jumla} = 30+30+30+35+35+35+38+40+40+40+40+40+45+45+45+50+50+50+50+50+50+50+55+55+60+60+60+60+65$ $\text{Jumla} = 1373$
Gawanya jumla ya alama kwa idadi ya alama.
$\text{Wastani} = \frac{\text{Jumla}}{\text{Idadi ya alama}} = \frac{1373}{29}$ $\text{Wastani} \approx 47.34$
Wastani wa alama ni $\boxed{\text{47.34}}$ .

2. Thamani ya Kati (Median)
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
Tafuta thamani ya kati.
Kwa kuwa kuna idadi isiyo ya kawaida ya alama ( $n=29$ ), thamani ya kati ni alama ya $\frac{n+1}{2}$ -th.
$\text{Nafasi ya thamani ya kati} = \frac{29+1}{2} = \frac{30}{2} = 15$
Alama ya 15 katika orodha iliyopangwa ni 45.
Thamani ya kati ya alama ni $\boxed{\text{45}}$ .

3. Njia (Mode)
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
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 $\boxed{\text{50}}$ .

Marks: 60, 30, 45, 50, 50, 45, 40, 60, 30, 35, 40, 50, 55, 60, 30, 50, 65, 42, 50, 45, 40, 35, 50, 30, 38, 55, 60, 40, 35, 50

Answer

Step-by-step solution

Jumlisha alama zote.

Gawanya jumla ya alama kwa idadi ya alama.

Panga alama kwa mpangilio wa kupanda (tayari tumefanya).

Tafuta thamani ya kati.

Hesabu marudio ya kila alama.

Alama inayoonekana mara nyingi zaidi ndiyo njia.

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