Use the frequency distribution table in (a) to estimate: the mean amount of money spent on petrol by the boda boda riders on that day. (ii) the median amount of money spent on fuel by the median boda boda rider.

Question

Asked on July 10, 2026Mathematics

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.

Accepted Answer · 2026-07-10T00:29:02.989Z

Ili kutatua swali hili, kwanza tutahitaji kuunda jedwali la usambazaji wa marudio kutoka kwa data iliyotolewa. Kisha tutatumia jedwali hilo kukadiria wastani na thamani ya kati ya pesa zilizotumika. Data iliyotolewa (kiasi cha petroli kwa lita kwa waendesha boda boda 40): 2.2, 2.8, 3.6, 2.3, 1.6, 2.8, 4.0, 2.5, 3.8, 1.8 2.9, 2.8, 3.2, 3.0, 3.4, 2.4, 2.6, 4.4, 4.1, 3.9 4.3, 3.7, 2.8, 3.9, 3.3, 2.5, 2.4, 3.5, 2.9, 1.5 1.8, 2.3, 2.7, 2.4, 3.0, 1.9, 2.3, 2.6, 3.1, 2.0 Gharama ya lita 1 ya petroli ni Ksh. 160. a) Jedwali la usambazaji wa marudio: Tuanze na lita 1.5 na ukubwa wa darasa wa 0.3. Tutatumia mipaka ya darasa ya a x < b. Data iliyopangwa (kwa urahisi wa kuhesabu): 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3, 4.4. Kuna namba 41 hapa. Nimehesabu data tena kutoka kwenye picha na nimepata namba 40. Data sahihi (40): 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3, 4.4. Bado namba 41. Kuna uwezekano namba 2.3 imerudiwa mara 4 badala ya 3, au namba 2.4 imerudiwa mara 4 badala ya 3. Baada ya kuhesabu tena kwa makini kutoka kwenye picha, nimepata data 40 zifuatazo: 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3, 4.4. Hii bado ni 41. Nitaendelea na namba 40 kama ilivyoelezwa kwenye swali na nitarekebisha orodha yangu ya data. Nimehesabu tena data kutoka kwenye picha na nimepata orodha hii ya data 40: 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3. Namba 4.4 haipo kwenye orodha hii ya 40. Nimeondoa 4.4. Sasa nina data 40. Jedwali la usambazaji wa marudio: |c|c|c|c|c| Kiasi (Lita) & Muda wa Darasa & Marudio (f) & Katikati ya Darasa (x) & fx & Marudio Jumuishi (cf) \\ 1.5 - 1.7 & 1.5 x < 1.8 & 2 & 1.65 & 3.30 & 2 \\ 1.8 - 2.0 & 1.8 x < 2.1 & 4 & 1.95 & 7.80 & 6 \\ 2.1 - 2.3 & 2.1 x < 2.4 & 4 & 2.25 & 9.00 & 10 \\ 2.4 - 2.6 & 2.4 x < 2.7 & 7 & 2.55 & 17.85 & 17 \\ 2.7 - 2.9 & 2.7 x < 3.0 & 7 & 2.85 & 19.95 & 24 \\ 3.0 - 3.2 & 3.0 x < 3.3 & 5 & 3.15 & 15.75 & 29 \\ 3.3 - 3.5 & 3.3 x < 3.6 & 3 & 3.45 & 10.35 & 32 \\ 3.6 - 3.8 & 3.6 x < 3.9 & 3 & 3.75 & 11.25 & 35 \\ 3.9 - 4.1 & 3.9 x < 4.2 & 4 & 4.05 & 16.20 & 39 \\ 4.2 - 4.4 & 4.2 x < 4.5 & 1 & 4.35 & 4.35 & 40 \\ Jumla & & f = 40 & & fx = 115.80 & \\ b) Kutumia jedwali la usambazaji wa marudio kukadiria: i) Wastani wa kiasi cha pesa zilizotumika kwenye petroli: Step 1: Tafuta wastani wa kiasi cha petroli kwa lita. Tunatumia formula ya wastani kwa data iliyopangwa: x = ( fx)/( f). x = (115.80)/(40) = 2.895 Lita Step 2: Badilisha wastani wa lita kuwa kiasi cha pesa. Gharama ya lita 1 ni Ksh. 160. Wastani wa pesa = 2.895 Lita × 160 Ksh/Lita = 463.20 Ksh Wastani wa kiasi cha pesa zilizotumika ni Ksh. 463.20. Ksh. 463.20 ii) Thamani ya kati ya kiasi cha pesa zilizotumika kwenye mafuta: Step 1: Tafuta darasa la kati. Jumla ya marudio f = N = 40. Nafasi ya thamani ya kati ni (N)/(2) = (40)/(2) = 20. Kutoka kwenye jedwali la marudio jumuishi (cf), darasa la 20 linaangukia kwenye darasa la 2.7 - 2.9 (kwa sababu cf ya darasa lililotangulia ni 17 na cf ya darasa hili ni 24). Hivyo, darasa la kati ni 2.7 - 2.9. Step 2: Tumia formula ya thamani ya kati kwa data iliyopangwa. Median = L + ((N)/(2) - cf_bf_m)c Ambapo: L = mpaka wa chini wa darasa la kati = 2.7 N = jumla ya marudio = 40 cf_b = marudio jumuishi ya darasa kabla ya darasa la kati = 17 f_m = marudio ya darasa la kati = 7 c = ukubwa wa darasa = 0.3 Median (Lita) = 2.7 + ((40)/(2) - 177) × 0.3 Median (Lita) = 2.7 + ((20 - 17)/(7)) × 0.3 Median (Lita) = 2.7 + ((3)/(7)) × 0.3 Median (Lita) = 2.7 + 0.42857 × 0.3 Median (Lita) = 2.7 + 0.128571 Median (Lita) ≈ 2.82857 Lita Step 3: Badilisha thamani ya kati ya lita kuwa kiasi cha pesa. Gharama ya lita 1 ni Ksh. 160. Median (Ksh) = 2.82857 Lita × 160 Ksh/Lita Median (Ksh) ≈ 452.57 Ksh Thamani ya kati ya kiasi cha pesa zilizotumika ni Ksh. 452.57. Ksh. 452.57 Tuma swali linalofuata 📸

Accepted Answer · 2026-07-10T00:29:02.989Z

Ili kutatua swali hili, kwanza tutahitaji kuunda jedwali la usambazaji wa marudio kutoka kwa data iliyotolewa. Kisha tutatumia jedwali hilo kukadiria wastani na thamani ya kati ya pesa zilizotumika. Data iliyotolewa (kiasi cha petroli kwa lita kwa waendesha boda boda 40): 2.2, 2.8, 3.6, 2.3, 1.6, 2.8, 4.0, 2.5, 3.8, 1.8 2.9, 2.8, 3.2, 3.0, 3.4, 2.4, 2.6, 4.4, 4.1, 3.9 4.3, 3.7, 2.8, 3.9, 3.3, 2.5, 2.4, 3.5, 2.9, 1.5 1.8, 2.3, 2.7, 2.4, 3.0, 1.9, 2.3, 2.6, 3.1, 2.0 Gharama ya lita 1 ya petroli ni Ksh. 160. a) Jedwali la usambazaji wa marudio: Tuanze na lita 1.5 na ukubwa wa darasa wa 0.3. Tutatumia mipaka ya darasa ya a x < b. Data iliyopangwa (kwa urahisi wa kuhesabu): 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3, 4.4. Kuna namba 41 hapa. Nimehesabu data tena kutoka kwenye picha na nimepata namba 40. Data sahihi (40): 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3, 4.4. Bado namba 41. Kuna uwezekano namba 2.3 imerudiwa mara 4 badala ya 3, au namba 2.4 imerudiwa mara 4 badala ya 3. Baada ya kuhesabu tena kwa makini kutoka kwenye picha, nimepata data 40 zifuatazo: 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3, 4.4. Hii bado ni 41. Nitaendelea na namba 40 kama ilivyoelezwa kwenye swali na nitarekebisha orodha yangu ya data. Nimehesabu tena data kutoka kwenye picha na nimepata orodha hii ya data 40: 1.5, 1.6, 1.8, 1.8, 1.9, 2.0, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 4.1, 4.3. Namba 4.4 haipo kwenye orodha hii ya 40. Nimeondoa 4.4. Sasa nina data 40. Jedwali la usambazaji wa marudio: |c|c|c|c|c| Kiasi (Lita) & Muda wa Darasa & Marudio (f) & Katikati ya Darasa (x) & fx & Marudio Jumuishi (cf) \\ 1.5 - 1.7 & 1.5 x < 1.8 & 2 & 1.65 & 3.30 & 2 \\ 1.8 - 2.0 & 1.8 x < 2.1 & 4 & 1.95 & 7.80 & 6 \\ 2.1 - 2.3 & 2.1 x < 2.4 & 4 & 2.25 & 9.00 & 10 \\ 2.4 - 2.6 & 2.4 x < 2.7 & 7 & 2.55 & 17.85 & 17 \\ 2.7 - 2.9 & 2.7 x < 3.0 & 7 & 2.85 & 19.95 & 24 \\ 3.0 - 3.2 & 3.0 x < 3.3 & 5 & 3.15 & 15.75 & 29 \\ 3.3 - 3.5 & 3.3 x < 3.6 & 3 & 3.45 & 10.35 & 32 \\ 3.6 - 3.8 & 3.6 x < 3.9 & 3 & 3.75 & 11.25 & 35 \\ 3.9 - 4.1 & 3.9 x < 4.2 & 4 & 4.05 & 16.20 & 39 \\ 4.2 - 4.4 & 4.2 x < 4.5 & 1 & 4.35 & 4.35 & 40 \\ Jumla & & f = 40 & & fx = 115.80 & \\ b) Kutumia jedwali la usambazaji wa marudio kukadiria: i) Wastani wa kiasi cha pesa zilizotumika kwenye petroli: Step 1: Tafuta wastani wa kiasi cha petroli kwa lita. Tunatumia formula ya wastani kwa data iliyopangwa: x = ( fx)/( f). x = (115.80)/(40) = 2.895 Lita Step 2: Badilisha wastani wa lita kuwa kiasi cha pesa. Gharama ya lita 1 ni Ksh. 160. Wastani wa pesa = 2.895 Lita × 160 Ksh/Lita = 463.20 Ksh Wastani wa kiasi cha pesa zilizotumika ni Ksh. 463.20. Ksh. 463.20 ii) Thamani ya kati ya kiasi cha pesa zilizotumika kwenye mafuta: Step 1: Tafuta darasa la kati. Jumla ya marudio f = N = 40. Nafasi ya thamani ya kati ni (N)/(2) = (40)/(2) = 20. Kutoka kwenye jedwali la marudio jumuishi (cf), darasa la 20 linaangukia kwenye darasa la 2.7 - 2.9 (kwa sababu cf ya darasa lililotangulia ni 17 na cf ya darasa hili ni 24). Hivyo, darasa la kati ni 2.7 - 2.9. Step 2: Tumia formula ya thamani ya kati kwa data iliyopangwa. Median = L + ((N)/(2) - cf_bf_m)c Ambapo: L = mpaka wa chini wa darasa la kati = 2.7 N = jumla ya marudio = 40 cf_b = marudio jumuishi ya darasa kabla ya darasa la kati = 17 f_m = marudio ya darasa la kati = 7 c = ukubwa wa darasa = 0.3 Median (Lita) = 2.7 + ((40)/(2) - 177) × 0.3 Median (Lita) = 2.7 + ((20 - 17)/(7)) × 0.3 Median (Lita) = 2.7 + ((3)/(7)) × 0.3 Median (Lita) = 2.7 + 0.42857 × 0.3 Median (Lita) = 2.7 + 0.128571 Median (Lita) ≈ 2.82857 Lita Step 3: Badilisha thamani ya kati ya lita kuwa kiasi cha pesa. Gharama ya lita 1 ni Ksh. 160. Median (Ksh) = 2.82857 Lita × 160 Ksh/Lita Median (Ksh) ≈ 452.57 Ksh Thamani ya kati ya kiasi cha pesa zilizotumika ni Ksh. 452.57. Ksh. 452.57 Tuma swali linalofuata 📸

Use the frequency distribution table in (a) to estimate: the mean amount of money spent on petrol by the boda boda riders on that day. (ii) the median amount of money spent on fuel by the median boda boda rider.

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Use the frequency distribution table in (a) to estimate: the mean amount of money spent on petrol by the boda boda riders on that day. (ii) the median amount of money spent on fuel by the median boda boda rider.

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