Summarize the products sold above c tion table using a class interval of 10 and starting with the smallest p 0727270764

Data zilizopangwa: 23, 26, 32, 36, 37, 38, 39, 39, 40, 40, 40, 40, 42, 42, 43, 43, 44, 45, 46, 46, 47, 47, 48, 48, 50, 50, 51, 51, 51, 51, 52, 53, 54, 55, 58, 58, 59, 59, 59, 60, 60, 60, 61, 61, 62, 65, 67, 67, 68, 69, 70, 71, 73, 74.
Thamani ndogo zaidi ni 23. Thamani kubwa zaidi ni 74.

Madarasa yatakuwa: 20-29, 30-39, 40-49, 50-59, 60-69, 70-79.

• 20-29: 23, 26 (Marudio = 2)
• 30-39: 32, 36, 37, 38, 39, 39 (Marudio = 6)
• 40-49: 40, 40, 40, 40, 42, 42, 43, 43, 44, 45, 46, 46, 47, 47, 48, 48 (Marudio = 16)
• 50-59: 50, 50, 51, 51, 51, 51, 52, 53, 54, 55, 58, 58, 59, 59, 59 (Marudio = 15)
• 60-69: 60, 60, 60, 61, 61, 62, 65, 67, 67, 68, 69 (Marudio = 11)
• 70-79: 70, 71, 73, 74 (Marudio = 4) Jumla ya marudio = $2+6+16+15+11+4 = 54$. Kuna makosa katika kuhesabu marudio. Hebu tuhesabu tena kwa uangalifu kutoka kwenye jedwali asili. Jumla ya wafanyakazi ni $5 \times 10 = 50$.

Hebu tuhesabu tena kwa uangalifu:

• 20-29: 23, 26 (2)
• 30-39: 38, 37, 39, 32, 39, 36 (6)
• 40-49: 40, 40, 40, 40, 42, 47, 47, 46, 45, 46, 44, 43, 48, 48 (14)
• 50-59: 55, 54, 58, 52, 50, 51, 50, 59, 51, 58, 53, 51, 59, 51, 59 (15)
• 60-69: 62, 67, 67, 65, 60, 60, 68, 69, 61 (9)
• 70-79: 71, 73, 74, 70 (4) Jumla ya marudio = $2+6+14+15+9+4 = 50$. Hii inalingana na idadi ya wafanyakazi.

Jedwali la usambazaji wa marudio:

b) Je, kampuni itaendelea na njia mpya ya kuuza bidhaa au la? (Thibitisha jibu lako)

Jumla ya bidhaa zilizouzwa = $55+38+54+58+52+71+40+50+62+23 + 48+50+42+67+37+51+40+67+65+40 + 39+59+47+60+26+47+51+46+58+53 + 45+40+68+69+73+32+46+39+51+59 + 74+44+51+43+60+48+59+61+36+70 = 2564$.

Idadi ya wafanyakazi = 50.
Wastani = $\frac{\text{Jumla ya bidhaa zilizouzwa}}{\text{Idadi ya wafanyakazi}} = \frac{2564}{50} = 51.2$.

Kigezo ni kwamba wastani unapaswa kuzidi 45.
Kwa kuwa $51.2 > 45$, kampuni inapaswa kuendelea na njia mpya ya kuuza bidhaa.

b) Ndiyo, kampuni inapaswa kuendelea na njia mpya ya kuuza bidhaa kwa sababu wastani wa bidhaa zilizouzwa kwa kila mfanyakazi ni $\boxed{\text{51.2}}$, ambayo inazidi 45.

c) Ni asilimia ngapi ya wafanyakazi wa mauzo watakaoachishwa kazi?

Wafanyakazi watakaoachishwa kazi ni wale waliouza bidhaa zisizozidi 45 (yaani, $\le 45$).
Kutoka kwenye data asili, wafanyakazi waliouza $\le 45$ ni:
23, 26, 32, 36, 37, 38, 39, 39, 40, 40, 40, 40, 42, 42, 43, 44, 45.
Idadi ya wafanyakazi hawa ni 17.

Jumla ya wafanyakazi = 50.
Asilimia = $\frac{\text{Idadi ya wafanyakazi watakaoachishwa kazi}}{\text{Jumla ya wafanyakazi}} \times 100\%$
Asilimia = $\frac{17}{50} \times 100\% = 34\%$.

c) Asilimia ya wafanyakazi wa mauzo watakaoachishwa kazi ni $\boxed{\text{34\%}}$.

KIPENGELE CHA 4

a) Msaidie mwalimu kubaini jumla ya idadi ya wale waliomchagua A na C mtawalia na hivyo kumsaidia kufikia hitimisho juu ya nani wa kumchagua kama mfuatiliaji wa darasa.

Jumla ya wanafunzi = 116.
Hebu $a = N(A \text{ pekee})$, $b = N(B \text{ pekee})$, $c = N(C \text{ pekee})$.
Hebu $ab = N(A \cap B \text{ pekee})$, $ac = N(A \cap C \text{ pekee})$, $bc = N(B \cap C \text{ pekee})$.
Hebu $abc = N(A \cap B \cap C)$, na $none = N(\text{Hakuna})$.

Kutoka taarifa:

1. $ac = 20$ (Waliomchagua A na C pekee)
2. $bc = 18$ (Waliomchagua B na C pekee)
3. $b = \frac{1}{2}a$
4. $N(B) = 42$
5. $c = 20$ (Waliomchagua C pekee)
6. $ac = none \implies none = 20$

Tunajua $N(B) = b + ab + bc + abc = 42$.
Kubadilisha $bc = 18$: $b + ab + 18 + abc = 42 \implies b + ab + abc = 24$.

Jumla ya wanafunzi = $a + b + c + ab + ac + bc + abc + none = 116$.
Kubadilisha maadili tunayoyajua:
$a + b + 20 + ab + 20 + 18 + abc + 20 = 116$.
$a + b + ab + abc + 78 = 116$.
$a + b + ab + abc = 38$.

Sasa tuna mfumo wa milinganyo:

i) $b + ab + abc = 24$

ii) $a + b + ab + abc = 38$

iii) $b = \frac{1}{2}a$

Badilisha (i) katika (ii): $a + 24 = 38 \implies a = 14$.
Sasa tumia (iii): $b = \frac{1}{2}(14) = 7$.

Sasa tunaweza kupata $ab + abc$:
$7 + ab + abc = 24 \implies ab + abc = 17$.

Taarifa "20 ticked on A and C" inamaanisha $N(A \cap C) = 20$.
$N(A \cap C) = ac + abc$.
Kwa kuwa $ac = 20$, basi $20 + abc = 20 \implies abc = 0$.
Hivyo, $ab = 17$.

Muhtasari wa kura zote:

• $N(A \text{ pekee}) = a = 14$
• $N(B \text{ pekee}) = b = 7$
• $N(C \text{ pekee}) = c = 20$
• $N(A \cap B \text{ pekee}) = ab = 17$
• $N(A \cap C \text{ pekee}) = ac = 20$
• $N(B \cap C \text{ pekee}) = bc = 18$
• $N(A \cap B \cap C) = abc = 0$
• $N(\text{Hakuna}) = none = 20$

• Jumla ya waliomchagua A ($N(A)$): $N(A) = N(A \text{ pekee}) + N(A \cap B \text{ pekee}) + N(A \cap C \text{ pekee}) + N(A \cap B \cap C)$ $N(A) = 14 + 17 + 20 + 0 = 51$.
• Jumla ya waliomchagua B ($N(B)$): $N(B) = N(B \text{ pekee}) + N(A \cap B \text{ pekee}) + N(B \cap C \text{ pekee}) + N(A \cap B \cap C)$ $N(B) = 7 + 17 + 18 + 0 = 42$. (Hii inalingana na $N(B)=42$ iliyotolewa)
• Jumla ya waliomchagua C ($N(C)$): $N(C) = N(C \text{ pekee}) + N(A \cap C \text{ pekee}) + N(B \cap C \text{ pekee}) + N(A \cap B \cap C)$ $N(C) = 20 + 20 + 18 + 0 = 58$.

Kura zilizopigwa: A = 51, B = 42, C = 58.
Mwanafunzi C ana kura nyingi zaidi.

a) Jumla ya waliomchagua A ni $\boxed{\text{51}}$ na jumla ya waliomchagua C ni $\boxed{\text{58}}$. Mwalimu anapaswa kumchagua C kama mfuatiliaji wa darasa kwa sababu ana kura nyingi zaidi.

b) Je, itakuwa rahisi kwa yule aliyechaguliwa kusimamia darasa? (Thibitisha jibu lako)

Mfuatiliaji aliyechaguliwa ni C.
Idadi ya wanafunzi wanaompinga C ni wale ambao hawakumchagua C.
Idadi ya wanafunzi wanaompinga C = Jumla ya wanafunzi - Jumla ya waliomchagua C
Idadi ya wanafunzi wanaompinga C = $116 - 58 = 58$.

Asilimia ya wanafunzi wanaompinga C = $\frac{\text{Idadi ya wanafunzi wanaompinga C}}{\text{Jumla ya wanafunzi}} \times 100\%$
Asilimia = $\frac{58}{116} \times 100\% = 50\%$.

Kigezo ni kwamba asilimia ya wanaompinga inapaswa kuwa chini ya 50%.
Kwa kuwa asilimia ya wanaompinga C ni 50%, ambayo sio chini ya 50%, haitakuwa rahisi kwake kusimamia darasa.

b) ❌ Hapana, haitakuwa rahisi kwa C kusimamia darasa. Asilimia ya wanafunzi wanaompinga C ni $\boxed{\text{50\%}}$, ambayo sio chini ya 50% kama inavyotakiwa kwa usimamizi rahisi.