NCERT Solutions Class 8 Maths Part 2 Chapter 5: Tales by Dots and Lines (Hinglish)

Ganita Prakash, Grade 8 Part 2, ke Chapter 5, Tales by Dots and Lines, ke andar ke sawaalon aur teeno Figure it Out ke jawaab. Page numbers book ke hisaab se hain (pages 103–134). Book ke graphs se li gayi readings anumaanit hain. Chhote notes: Part 2 Chapter 5 ke notes.

The Balancing Act (pages 103–112)

Koi do sankhyaon ka mean. Wo hamesha dono ke theek beech hota hai: 3 aur 7 ka 5, 8 aur 9 ka 8.5.

Page 103 ke samoohon ke mean. 6, 7, 8: mean 7. 3, 6, 9: mean 6. 2, 4, 9: mean 5. 4, 11, 15: mean 10. Page 104 par: 11, 13, 17, 19: mean 15. 5, 6, 15, 16: mean 10.5. 10, 10, 11, 17: mean 12. 3, 5, 10, 12: mean 7.5.

Mean kendra kaise hai? LHS = RHS jaanchiye. Har samooh mein mean se neeche ki kul doori upar ki kul doori ke barabar hai. 6, 7, 8: 1 aur 1. 3, 6, 9: 3 aur 3. 4, 11, 15: 6 aur 1 + 5 = 6. 11, 13, 17, 19: 4 + 2 = 6 aur 2 + 4 = 6. 5, 6, 15, 16: 5.5 + 4.5 = 10 aur 4.5 + 5.5 = 10. 3, 5, 10, 12: 4.5 + 2.5 = 7 aur 2.5 + 4.5 = 7.

Kya ek se zyada kendra ho sakte hain? Nahi. Bindu upar khiskaane par neeche ki har doori badhti hai aur upar ki har doori ghatti hai, isliye jod barabar nahi reh sakte; neeche khiskaane par ulta hota hai.

Value jodna ya hataana. Mean se badi value jodne par mean badhta hai, chhoti par ghatta hai, aur barabar par waisa hi rehta hai. Mean se badi value hataane par mean ghatta hai, chhoti hataane par badhta hai, aur barabar hataane par kuch nahi badalta. Barabar hisse ki bhasha mein: barabar hisse se zyada laane waale log judte hain to sabka hissa badhta hai; unke jaane par ghatta hai.

Mean badle bina values jodna ya hataana. Do values: unhe mean se barabar doori par dono taraf chuniye (mean 9 ho to 7 aur 11 jodiye, ya 8 aur 10 hataaiye), ya dono mean ke barabar. Teen values: dooriyaan phir bhi santulit honi chahiye, jaise 7, 7 aur 13. Do upar aur ek neeche: jaise 10 aur 11 ke saath 6, kyonki 1 + 2 = 3.

Relatively unchanged. 8, 3, 10, 13, 4, 6, 7, 7, 8, 8, 5 ka mean 79 ÷ 11 ≈ 7.18 hai. Har value 10 badhaane par jaldi wala tareeka hai mean mein 10 jodna: lagbhag 17.18. Har value se 2 ghataane par jod 2n ghatta hai, isliye mean 2 ghatta hai; barabar hisse ki bhasha mein, sab 2 lauta dein to har hissa 2 kam. Har value do guni karne par mean do guna.

Median se chhed-chhaad. Median se badi value jodne par wo badhta hai ya waisa hi rehta hai; chhoti value se ghatta hai ya waisa hi rehta hai. Median 8 wale data mein 11 jodne par median (8 + 11) ÷ 2 = 9.5 ho jaata hai.

Aapki class ka ausat parivaar size. Har vidyaarthi ke parivaar ka size likhiye, frequency table banaaiye, har size ko uski frequency se guna kijiye, jodiye aur vidyaarthiyon ki sankhya se bhaag dijiye. Book ki class ke liye mean 188 ÷ 36 ≈ 5.22 hai, aur median, running total se mili 18vi aur 19vi values, 5 hai.

Spreadsheet. Farooq ke Maths ke marks E5 mein hain. Cell B7 mein 27 hai, Gowri ke Odia ke marks. Ashwin ke Telugu (31), English (33) aur Maths (34) mein 30 se zyada marks hain. Science ka class ausat =AVERAGE(G2:G23) hai, lagbhag 33.14. Odia ka class ausat, lagbhag 31.23, Telugu ke lagbhag 33.59 se zyada nahi hai. Baaki ausat: English 32.64, Maths 34.14 aur Social Science 31.36. Total =SUM(B2:G2) aur aage ki rows se aate hain: jaise Ratna 200, Nagesh 250, Farooq 266 aur sabse zyada Aishwarya 273, aur sabse kam Shravan 102.

Figure it Out (pages 113–116)

1. (i) Pehli 50 prakritik sankhyaayein: 1275 ÷ 50 = 25.5. (ii) Pehli 50 visham sankhyaayein: 2500 ÷ 50 = 50. (iii) 4 ke pehle 50 gunaj: 5100 ÷ 50 = 102. Barabar antar wali sankhyaon ka mean pehli aur aakhri value ka ausat hota hai aur median ke barabar hota hai; 4 ke gunajon ka mean 1 se 50 ke mean ka 4 guna hai.

2. Plot mein 4, 7, 8, 8, 9, 9, 9, 9, 9 aur 11 hain. 9 se neeche ki dooriyaan 5 + 2 + 1 + 1 = 9 jodti hain aur upar 2, isliye chhoota bindu 9 se 7 upar hona chahiye: 16.

3. (i) Dobara naapne ki zaroorat nahi: joote utaarne se har oonchaai 1 cm kam hoti hai, isliye mean 1 cm ghatta hai. (ii) (d) 149.2 cm.

4. Album A. Iske gaane 5, 5, 5.25, 5.5, 5.75, 6 aur 6.5 minute ke hain, isliye mean 39 ÷ 7 ≈ 5.57 hai. B aur C ke zyaadatar gaane 5 minute se chhote hain, isliye unke mean (lagbhag 2.4 aur 3.9) 5.57 se bahut kam hain.

5. Kram mein 16 values ke beech mein 41 aur 41 hain, isliye median 41 hai. (i) Koi bhi ek value: nayi beech wali value phir bhi 41 hai. (ii) Do values, ek 41 se zyada nahi aur ek 41 se kam nahi, jaise 30 aur 60. (iii) Koi bhi ek value hataayi ja sakti hai.

6. (i) Kabhi sach nahi: chhoti value hataane par median ooncha ho jaata hai (1, 2, 3, 4, 5 se 2, 3, 4, 5, median 3.5) ya waisa hi rehta hai (1, 3, 3, 3, 5 se 3, 3, 3, 5, median 3). (ii) Hamesha sach. (iii) Kabhi-kabhi sach: do neeche aur do upar ki values median nahi badalti, par chaar badi values use badha deti hain. (iv) Kabhi sach nahi: chaar chhoti values median ghata deti hain ya waisa hi chhodti hain.

7. 10.375 × 8 = 83, aur 8 + 13 + 10 + 4 + 5 + 20 + 10 = 70, isliye y = 13.

8. Jod = 134 × 15 = 2010.

9. Kram mein baaki das values 8, 8, 12, 18, 25, 29, 35, 39, 47, 73 hain. 11 values mein median chhathi value hai, jo 29 tabhi hogi jab p kam se kam 29 ho. Isliye p (iii) 40, (iv) 100, (v) 29, (vi) 47 ya (vii) 30 ho sakta hai, par 10 ya 25 nahi.

10. (i) 42 vidyaarthiyon ne kul 193 baar cycle chalaayi, isliye mean lagbhag 4.6 hai. (ii) 21vi aur 22vi values dono 4 hain: median 4. (iii) (a) Sahi nahi: 3 vidyaarthiyon ne cycle nahi chalaayi. (b) Sahi: zyaadatar ne 2 se 8 baar chalaayi. (c) Sahi: 7 din mein 8 ya 10 rides waalon ne kisi din ek se zyada baar cycle chalaayi. (d) Sahi nahi: un 5 ne to zaroor, par doosron ne bhi kisi din do baar chalaayi ho sakti hai. (e) Har value 1 badhti hai, isliye mean lagbhag 5.6 aur median 5 ho jaata hai.

11. 62 vidyaarthi: nyuntam 1 phenk, adhiktam 10. Mean = 473 ÷ 62 ≈ 7.63 phenk. Median: 31vi aur 32vi values dono 8 hain, isliye 8 phenk. Zyaadatar vidyaarthiyon ko 6 se 10 phenk lage.

Visualising and Interpreting Data (pages 116–122)

Kya dono taapmaan graph ek hi jaankaari dikhaate hain? Haan: wahi mahine ka adhiktam taapmaan, columns aur rekhaon mein. Aage sochiye: Kerala samudra ke paas aur bhoomadhya rekha ke kareeb hai, jabki Punjab andar ki or aur zyada uttar mein, jisse wahaan garmi zyada garam aur sardi zyada thandi hoti hai; Haryana, Delhi aur Rajasthan jaise andar ke uttari rajyon ka trend Punjab jaisa hai. Mahine ke nyuntam taapmaan ka plot Punjab ki sardi mein bahut neeche jaata, jabki Kerala ka lagbhag sapaat rehta.

Launch ka data kaise jama hua hoga? Har saal bheji gayi har cheez ke record se, jo desh batate hain aur UN Office for Outer Space Affairs rakhta hai. Sahi nishkarsh: doosra (2022–24 mein USA ne lagbhag teen-chauthaai bheji) aur chautha (2024 mein China aur Russia ne milkar lagbhag 400). Galat: ginti har saal nahi badhi, aur graph Nepal ke baare mein kuch nahi batata. Do guni se zyada: 2016 se 2017 (lagbhag 230 se 476) aur 2019 se 2020 (lagbhag 604 se 1,257).

Baarish ka data. Har shehar mein kai saalon tak roz baarish naapkar aur har mahine ka kul ausat lekar banta hai. Kovalam, Udupi aur Mumbai paschimi tat par hain aur dakshin-paschim monsoon se June se August mein bhaari baarish paate hain; Rameswaram aur Chennai poorvi tat par hain aur zyaadatar baarish uttar-poorvi monsoon se October se December mein paate hain; Puri mein July se September mein sabse zyada.

Figure it Out (pages 122–123)

1. Aade mein din aur khade mein graahak lagaaiye, ek rekha aane waalon ki aur ek khareedne waalon ki. Sunday sabse vyast hai aur Wednesday sabse shaant; Tuesday ko zyada log aaye par kam ne khareeda.

2. (i) Har shehar ke mausam kendra par kai saalon tak har mahine baarish wale din giniye, phir har mahine ka ausat lijiye. (ii) Graph dekhiye. (iii) Graph se New Delhi: January se December tak lagbhag 1, 1.5, 1.5, 1, 1.5, 4, 10, 10, 4, 1, 0.5 aur 1 din, saal mein lagbhag 37. (iv) Sabse zyada Port Blair, saal mein lagbhag 126 din; sabse kam New Delhi, lagbhag 37, aur Rameswaram lagbhag 42. (v) New Delhi ka barsaati mausam July aur August hai, June se September ke beech; Rameswaram ka October se December.

2 (janm, book mein phir se 2 number). (i) Pattern har saal dohraata hai: August se October mein janm lagbhag 20 lakh mahina tak badhte hain aur April ke aas-paas lagbhag 14 se 15 lakh tak girte hain; February chhota mahina hone se bhi kam rehta hai. (ii) July 2017 mein lagbhag 17.7 lakh (1.77 million). (iii) April 2017 se March 2020, teen saal ke mahine. (iv) January 2018 mein lagbhag 16.7 lakh, January 2019 mein 17.5 lakh aur January 2020 mein 17.7 lakh: har saal thoda badhta hua. (v) 2019 ke baarah mahine jodne par lagbhag 2.1 crore (21 million) janm.

Infographic aur strips (pages 123–127)

Chaawal ya gehun. (i) Karnataka laal rekha ke dakshin mein chaawal khaane wale padosiyon (Goa +57, Kerala +79, Tamil Nadu +85, avibhajit Andhra +92) ke beech hai aur uska rang unse milta hai, isliye lagbhag +70 se +80 ka anumaan theek hai. (ii) Chaawal: Manipur (+100), Nagaland (+99), Mizoram (+97), Tripura (+96) aur Meghalaya (+95). (iii) Gehun: Rajasthan (−93), Haryana (−81), Punjab (−78), Madhya Pradesh (−60) aur Delhi (−45). (iv) Lagbhag santulit: Bihar (+3), Maharashtra (−15), Uttarakhand (−18) aur Himachal Pradesh (−19).

Manoj ki strips. (i) Halka neela: sona; hara: khaana; baingani: nahaana, kapde pehenna, yoga ya kasrat; gehra grey: safar; peela: class, padhaai aur homework; naarangi: dost, shauk, media aur parivaar. (ii) Beech wali strip Friday hai (9:00 se 4:30 tak school), daayin Saturday (12:30 tak class, jhapki, aur raat 9:30 par sona) aur baayin Sunday (koi class nahi, school se pehle raat 8:30 par jaldi sona). (iii) Shaayad Sunday ko, lagbhag 1:30 se 4:30 pm: dosto ke saath teen ghante, theek pehle aur baad mein safar ke saath. (iv) 12:30 pm par, 1:00 tak lunch aur 1:30 tak break. (v) Wo roz lagbhag 10½ ghante sota hai, tay samay par khaata hai, aur Friday ko class aur padhaai mein lagbhag 7 ghante par Sunday ko sirf 2 ghante lagaata hai.

Apni strips. School ke din ki strip mein school ke ghante aur safar dikhenge; chhutti ki strip mein zyada neend, khel aur parivaar ka samay; kisi bade ki strip mein kaam ke ghante, safar aur ghar ke kaam. Dekhiye rang kahaan ikatthe hote hain.

Umar ke saath neend. Neend 6 saal par lagbhag 9.5 ghante se 30 se 50 ke beech lagbhag 8 ghante tak ghatti hai, phir baad ki umar mein lagbhag 8.5 ghante tak badhti hai.

Figure it Out (pages 127–132)

1. Mean grids. (i) 7, 12, 11 / 14, 10, 6 / 9, 8, 13: har row, column aur vikarn ka jod 30, yaani ausat 10. (ii) Haan: grid ghumaane ya palatne se, ya har sankhya ko 10 se do guni doori par le jaane se (4, 14, 12 / 18, 10, 2 / 8, 6, 16), saare ausat 10 hi rehte hain. Beech mein 10 hi rehna chahiye.

2. (i) 7, 8, 9; ya 2, 10, 12. (ii) 12, 14, 17, 19; ya 15, 15, 16, 16. (iii) 10, 12, 14, 16, 16; ya 13, 13, 14, 14, 14 (jod 68). (iv) 1, 2, 3, 4, 5, 6; ya 2, 4, 6, 6, 8, 10. (v) 1, 2, 3, 4, 5, 30; ya 1, 1, 1, 1, 2, 100.

3. Chhah values mein teesri aur chauthi ka ausat 13 hona chahiye, isliye wo 13 aur 13 hain, ya 12 aur 14. 13 aur 13 ho to teesri khaali jagah 13 tak koi bhi ginti ki sankhya (13 tareeke). 12 aur di gayi 14 ho to khaali jagah 12, 1 se 12 tak koi sankhya, aur 14 se upar koi bhi sankhya, isliye anant sambhaavnaayein hain.

4. Chhah values ka jod 6 × 6.5 = 39 hona chahiye; diye gaye chaar ka jod 35 hai, isliye khaali jagahon ka jod 4: 1 aur 3, 2 aur 2, ya 3 aur 1, yaani 3 sambhaavnaayein.

5. Teeno galat hain. (i) 2 aur 4 ka ausat 3 hai, jo visham hai; aam taur par (2a + 2b) ÷ 2 = a + b, jo tabhi sam hai jab a + b sam ho. (ii) 5 aur 10 ka ausat 7.5 hai; (5a + 5b) ÷ 2 = 5(a + b) ÷ 2. (iii) 5, 5, 5, 5 aur 10 ka ausat 6 hai; 5a, 5b, 5c, 5d aur 5e ka ausat a + b + c + d + e hai, koi bhi poorn sankhya.

6. (i) Sirf (c) sahi hai: do nayi oonchaiyaan chahiye, par kisi aur ko dobara naapne ki zaroorat nahi; mean badh, ghat ya waisa hi reh sakta hai. (ii) (b): naye vidyaarthiyon ka ausat 150.5 cm hai, 150.2 se zyada, isliye mean thoda badhkar (24 × 150.2 + 149 + 152) ÷ 26 ≈ 150.22 cm ho jaata hai. (iii) (d): class ki oonchaiyon ke bina hum nahi jaante ki 149 aur 152 median ke mukaable kahaan hain.

7. Nahi. 17 se neeche ki dooriyon ka jod 13 aur upar ka 31 hai, isliye 17 santulan nahi karta; 25 values ka jod 443 hai, mean 17.72.

8. Kul badlaav −2 + 1 + 1 = 0 kg hai, isliye mean 65.3 kg hi rehta hai. Median badal bhi sakta hai aur nahi bhi, ye is par nirbhar hai ki kinke vazan badle, isliye pakka nahi keh sakte.

9. (i) Gujarat, Uttar Pradesh aur West Bengal ka graph dekhiye. (ii) 2020 ke baad zyaadatar rajyon mein daam badhe; Mizoram ke daam poore samay sabse zyada rahe, ₹29.80 tak. (iii) Gujarat 2024 tak lagbhag ₹13 aur ₹16.50 ke beech raha aur 2025 mein ₹19.20 par uchhla, jabki Uttar Pradesh lagaataar badhkar 2024 mein ₹26.90 tak gaya, phir ₹24.81 par aaya. (iv) West Bengal, ₹9.47 se ₹23.99, yaani ₹14.52 ki badhat. (v) Jaise, rajyon ke beech namak ke daam itne alag kyon hain.

10. (i) Sahi: 1983 mein lagbhag 83% graameen gharon mein kerosene aur lagbhag 64% shehri gharon mein bijli thi. (ii) Sahi. (iii) Galat: 2000 mein lagbhag 90% shehri ghar bijli istemaal karte the; lagbhag 10% kerosene. (iv) Galat: graph roshni ka mukhya srot dikhaata hai, bijli katna nahi.

11. (i) Lagbhag 2 ghante (2 se thoda zyada). (ii) (d) 14 saal. (iii) (a) Sahi nahi: 15 par lagbhag 1 se 1¼ ghante, 10 saal wale samay ka lagbhag aadha, do guna nahi. (b) Sahi nahi: graph ausat dikhaata hai, isliye kuch graameen 15 saal ke bachche ek ghante se kam bhi de sakte hain.

12 aur 13. Project. Kai dinon tak har aadha ghanta 48 boxon ki strip par likhiye, har activity ka ausat samay nikaaliye, aur ‘ausat din’ ki strip banaaiye. Neend ke liye parivaar ke har sadasya ki raat ki neend aur jhapkiyaan jodiye, aur bachchon, badon aur buzurgon ka ausat aur median milaaiye. School ke samay ke liye shuru aur khatm hone ka samay aur break ki lambaai likhkar unke mean aur median ki tulna kijiye.

14. Neeche ki rekhaayein suryoday hain aur upar ki suryaast. (i) Kibithu: January mein suryoday lagbhag 5:50 am, suryaast lagbhag 4:30 pm, lagbhag 10½ ghante ka din. (ii) Srinagar, June mein lagbhag 14½ ghante ki roshni. (iii) Kanyakumari ke din ki lambaai mushkil se badalti hai (lagbhag 11¾ se 12½ ghante), jabki uttar ki jagahon par kahin zyada badalti hai; aur Kibithu ka ghadi ka samay Ghuar Moti se lagbhag 1¾ ghante pehle hai kyonki poora desh ek hi samay rakhta hai.

15. (i) Purnima lagbhag 13 taareekh ko thi: chaand suryaast ke paas ugta tha (13 ko lagbhag 17:25) aur suryoday ke paas doobta tha. Amavasya lagbhag 28 taareekh ko thi: chaand Suraj ke saath ugta tha (lagbhag 06:15) aur lagbhag 17:00 par doobta tha. (ii) Chandroday aur chandraast har din der se hote hain, lagbhag 35 se 65 minute, ausatan 50 minute, isliye ek din chandraast nahi hota (6 taareekh) aur ek din chandroday nahi hota (21 taareekh), jab samay aadhi raat paar kar jaata hai.