Class 7 Maths Part 2 Chapter 5 NCERT Solutions Hinglish mein: Connecting the Dots…

Ganita Prakash Grade 7 (2026-27) ke Part 2 Chapter 5, Connecting the Dots…, ke har sawaal ka jawab: andar ke sawaal, har Figure it Out, Try This aur Math Talk sawaal, projects, aur number lock puzzle. Page numbers book se milte hain (pages 97–135). Book ke graphs se padhi gayi values andaaze hain, isliye tumhari reading mein thoda fark chalega. Chhote notes: Part 2 Chapter 5 ke notes.

Sawaal aur statements (pages 97–98)

5 feet aur 6 feet lambaai se har dost ka gender andaaza lagao. Zyaadatar log sochte hain ki 5 feet waala dost aurat hai aur 6 feet waala aadmi, kyunki aadmi aksar auraton se lambe hote hain. Andaaza galat bhi ho sakta hai; ye batata hai ki kya hone ki sambhaavna zyaada hai, kya pakka hai ye nahi. Yahi statistical thinking hai.

Math Talk: kaunse statistical sawaal hain?

• (a) India mein tennis ball ka daam: statistical. Daam dukaan aur brand ke hisaab se badalta hai, isliye data chahiye.
• (b) Is gali ke kutton ki umar: statistical. Har kutte ki umar alag hai.
• (c) Tumhari class mein kitne hisse ko pahaadi pe chadhna pasand hai: statistical. Har student se poochha jaata hai, aur jawab alag hote hain.
• (d) “Kya tumhe padhna pasand hai?”: statistical nahi. Ek insaan ek jawab deta hai.
• (e) Is deewar mein lagbhag kitni eentein hain: statistical nahi. Ek deewar ki ek hi ginti hai, jo gin kar ya andaaze se milti hai.
• (f) Kal ke match ke sabse achhe bowler waala sawaal: statistical. Isme har bowler ke aankde chahiye, jaise wickets aur diye gaye run, jo alag alag hain.
• (g) Pichhle saal Barmer mein baarish ka pattern: statistical. Isme kai dinon ya mahinon ki baarish ka data chahiye.

Representative values (pages 98–100)

Pehli series mein kisne behtar khela? Shubman ne 0, 17, 21 aur 90 banaaye; Yashasvi ne 67, 55, 18 aur 35. Akela sabse bada score, 90, Shubman ka hai. Yashasvi ne kul zyaada run banaaye, 128 ke mukaable 175, aur wo zyaada tikau tha: uske score 67 − 18 = 49 run ke daayre mein the, Shubman ke 90 − 0 = 90 ke. Dono ne 4 baar batting ki, isliye total ki tulna theek hai, aur kul milaakar Yashasvi behtar raha.

Doosri series ke baare mein Vaishnavi ki baat pe tum kya sochte ho? Ye theek nahi. Shubman ke 110 run 5 match se aaye, par Yashasvi ke 96 run sirf 4 se, isliye total ko seedhe compare nahi kar sakte.

Math Talk: kya ek number numbers ke group ko dikha sakta hai? Haan, mean jaisi representative value. Shubman: 110 ÷ 5 = 22 run har match. Yashasvi: 96 ÷ 4 = 24 run har match. Isliye is series mein Yashasvi behtar raha. (Book mein 110 ÷ 5 = 21 chhapa hai; sahi value 22 hai.)

Kis group mein har member ko zyaada amrood milenge? Shreyas ka group: 3 + 8 + 10 + 5 + 4 = 30 amrood, to 30 ÷ 5 = 6 har ek. Parag ka group: 5 + 4 + 6 + 3 + 4 + 8 = 30 amrood, to 30 ÷ 6 = 5 har ek. Shreyas ke group ke har member ko ek zyaada milta hai.

Roz gudhal ke phoolon ka average. (2 + 7 + 9 + 4 + 3) ÷ 5 = 25 ÷ 5 = 5 phool roz.

Figure it Out (page 101)

1. Shreyas ki ball uchhaal. 6 + 2 + 9 + 5 + 4 + 6 + 3 + 5 = 8 koshishon mein 40 baar, isliye average 40 ÷ 8 = 5 baar hai.

2. Khud karke dekho. Kam se kam 7 koshishein likho, uchhaal jodo aur koshishon ki ginti se bhaag do. Jaise 4, 7, 3, 6, 5, 8 aur 2 uchhaal se 35 ÷ 7 = 5 har koshish.

3. Ek hafte mein paudhe ke phool. 7 din tak roz naye phool gino, jodo aur 7 se bhaag do. Jaise 3, 5, 4, 6, 2, 5 aur 3 phool se 28 ÷ 7 = 4 phool roz.

4. Average mein kaun tez bhaaga? Nikhil: 17 + 18 + 17 + 16 + 19 + 17 + 18 = 122 s. Sunil: 20 + 18 + 18 + 17 + 16 + 16 + 17 = 122 s. Dono ke mean 122 ÷ 7 ≈ 17.43 s hain, isliye average mein koi bhi tez nahi. Nikhil thoda zyaada tikau tha, 16 se 19 s, jabki Sunil 16 se 20 s tak raha.

5. Average enrolment. (1555 + 1670 + 1750 + 2013 + 2040 + 2126) ÷ 6 = 11154 ÷ 6 = 1859 students.

Know your onions (pages 101–104)

Pyaaz kahan mehenga hai, aur har daave ke baare mein tum kya sochte ho?

• Khushboo sirf sabse ooncha daam, ₹60, dekhti hai aur baaki gyaarah mahine chhod deti hai.
• Nafisa ke total yahan theek compare hote hain, kyunki dono shehron ka 12 mahine ka data hai: Yahapur ₹458, Wahapur ₹450.
• Vishal sirf oonche daam dekhta hai (Wahapur ke 52, 53 aur 60; Yahapur ke 56 aur 59) aur baaki chhod deta hai.
• Sampat mahine waar compare karta hai: 6 mahine Yahapur mehenga, 5 mahine Wahapur, aur June mein barabar.
• Jithin ke fark, 35 aur 43, dikhate hain ki Wahapur ke daam zyaada badalte hain; ye nahi batate ki kaunsa shehar mehenga hai.

Sab milaakar Yahapur mein pyaaz thoda mehenga hai, jaise neeche ke mean bhi dikhate hain.

Data compare karne ke aur tareeke. Har shehar ka mean ya median, dot plot, ya mahinon ka double bar graph.

Kya dot plot saara data dikhata hai? Saare 24 daam dots ki tarah dikhte hain, isliye koi value nahi khoti, par mahine nahi dikhte. Kya isse Yahapur ka January ka daam bata sakte ho? Nahi. Dot plot values ko sort kar deta hai aur unka kram kho jaata hai.

Pyaaz ka average daam. Yahapur: 458 ÷ 12 ≈ ₹38.17 kilo. Wahapur: 450 ÷ 12 = ₹37.50 kilo. Average mein Yahapur mein pyaaz thoda mehenga hai.

Math Talk: tum aur kya sochte ho? Khule sawaal, jaise: dono shehron mein October aur November mein daam sabse oonche kyun hain? Kya dono shehar paas paas hain? Kya baarish ya fasal ka mausam daam badalta hai?

Outliers aur median (pages 105–109)

Har parivaar ki average lambaai; kya Yaangba ka parivaar lamba hai? Yaangba ka parivaar: 986 ÷ 6 ≈ 164.3 cm. Poovizhi ka parivaar: 801 ÷ 5 = 160.2 cm. Hum nahi keh sakte ki Yaangba ka parivaar lamba hai. Poovizhi ke parivaar ke paanch mein se chaar log 164.3 cm se lambe hain; unka mean sirf ek chhote bachche ki wajah se kam hai.

Kya median lambaai ko behtar dikhata hai? Haan, Poovizhi ke parivaar ke liye. Sort karne pe 118, 165, 170, 173, 175 ka median 170 cm hai, jo zyaadatar parivaar ke paas hai. Yaangba ka parivaar, 155, 160, 164, 165, 169, 173, ka median (164 + 165) ÷ 2 = 164.5 cm hai, jo uske mean ke lagbhag barabar hai.

118 ke bina Poovizhi ka data. Mean 683 ÷ 4 = 170.75 cm; median (170 + 173) ÷ 2 = 171.5 cm. Mean 10 cm se zyaada badhta hai par median sirf 1.5 cm, yaani outlier ne zyaadatar mean pe asar daala tha.

Padhi gayi chhoti kahaaniyan: pehle andaaza, phir mean aur median. Ek student ne 40 padhi, isliye ummeed karo ki mean median se zyaada hoga. 15 values 6, 3, 0, 8, 2, 5, 15, 7, 12, 10, 40, 5, 0, 1 aur 8 hain, jinka jod 122 hai, isliye mean 122 ÷ 15 ≈ 8.13 hai. Sort karne pe: 0, 0, 1, 2, 3, 5, 5, 6, 7, 8, 8, 10, 12, 15, 40. Aathvi value, 6, median hai.

Kaunsi value outlier hai? 40. Iske bina mean 82 ÷ 14 ≈ 5.86 aur median (5 + 6) ÷ 2 = 5.5 hai. Mean 2 se zyaada gira, median sirf 0.5.

Monday se Sunday tak akhbaar ke panne. 16 + 18 + 20 + 22 + 26 + 16 + 10 = 128, isliye mean 128 ÷ 7 ≈ 18.29 hai. Sort karne pe: 10, 16, 16, 18, 20, 22, 26, isliye median 18 hai.

Math Talk: har case ko ek example se milaao. (a) Mean aur median paas: akhbaar ke panne, 18.29 aur 18. (b) Mean < median: Poovizhi ke parivaar ki lambaai, 160.2 < 170. (c) Mean > median: chhoti kahaaniyan, 8.13 > 6.

Math Talk: dono taraf outliers. 20, 21, 22 aur 23 lo, jinka mean aur median 21.5 hai. Ek neeche ka outlier 1 aur ek upar ka outlier 50 jodo: data 1, 20, 21, 22, 23, 50 ka mean 137 ÷ 6 ≈ 22.83 aur median (21 + 22) ÷ 2 = 21.5 hai. Median nahi hilta. Dono outliers mean ko ulti dishaon mein kheenchte hain aur kuch had tak ek doosre ko kaat dete hain, aur mean us outlier ki taraf khisakta hai jo zyaada door hai (50 upar 28.5 door hai, 1 neeche 20.5). Agar dono barabar door hon, jaise 0 aur 43, to mean 21.5 hi rehta hai.

Sire aur saar (pages 109–110)

Tumhari class kitni lambi hai? Ek beech ki value aur phailaav do: mean aur median, sabse chhoti aur sabse lambi lambaai, aur ho sake to ek dot plot. Book ki Grade 5 class ke liye: “Class average mein lagbhag 145 cm lambi hai, 128 cm se 158 cm tak.”

Class ki average lambaai se kitne students lambe hain? 28 lambaaiyon ka jod 4046 cm hai, isliye class ka mean lagbhag 144.5 cm hai (book mein 144.4). 15 students lambe hain. Unme kitne ladke? 8: 145, 146, 146, 147, 150, 154, 155 aur 158 cm. Baaki 7 ladkiyan hain.

Ek minute kitna lamba hai? Dono groups compare karo. Dono groups 60 s ke aas paas kendrit hain. Group A ka mean 58.21 s aur median 60 s hai; iska mean median se neeche hai kyunki kuch bachchon ne aankhein bahut jaldi khol di, 40 ke shuruaati second mein. Group B ka mean 59.28 s aur median 59.5 s hai, lagbhag barabar, aur iski values 58–61 s ke aas paas zyaada sati hui hain. Dono lagbhag 25 second mein phaile hain (Group A lagbhag 42 se 68 s, Group B lagbhag 47 se 71 s), isliye kai bachche ek minute se 10 second ya zyaada door the. Group B ne thoda behtar kiya.

Zero median run (page 111)

Kya team ke 407/10 hone pe bhi batsmen ka median run 0 ho sakta hai? Haan. England ke gyaarah batsmen ne 19, 0, 0, 22, 158, 0, 184, 5, 0, 0 aur 0 run banaaye, yaani 388 run, aur 19 extras milaakar 407. Sort karne pe: 0, 0, 0, 0, 0, 0, 5, 19, 22, 158, 184. Chhati value 0 hai, isliye median 0 hai. Mean (407 − 19) ÷ 11 ≈ 35.27 run hai, jise do badi innings ne sambhaala.

Zero ya koi value nahi. Player ne Match 5 mein batting nahi ki, isliye 6 se bhaag do: (57 + 13 + 0 + 84 + 51 + 27) ÷ 6 = 232 ÷ 6 ≈ 38.67 run har match.

Sita ke aam. Sirf mausam, March se July, lo: 8, 24, 41, 16 aur 5. Mean 94 ÷ 5 = 18.8 aam har mahine hai, aur 5, 8, 16, 24, 41 ka median 16 hai.

Figure it Out (pages 112–113)

1. Pyaaz ke daam ka median. Yahapur sort karne pe: 24, 25, 26, 28, 30, 35, 39, 43, 44, 49, 56, 59, isliye median (35 + 39) ÷ 2 = ₹37 hai. Wahapur sort karne pe: 17, 19, 23, 30, 35, 38, 39, 42, 42, 52, 53, 60, isliye median (38 + 39) ÷ 2 = ₹38.5 hai. Median se Wahapur thoda ooncha hai, mean se Yahapur; dono shehar bahut paas hain.

2. Paaltu aur ghar ke jaanwar. Do gair haazir students ki koi value nahi, isliye 20 values hain jinka jod 72 hai. Mean 72 ÷ 20 = 3.6. Sort karne pe: 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 8, 10, 25, isliye median (2 + 2) ÷ 2 = 2 hai. Zyaadatar students ke paas 0 se 5 jaanwar hain, aur 6 ke paas ek bhi nahi. 25 upar ka outlier hai, aur 8 aur 10 bhi oonche hain, isliye mean median se kaafi upar hai; median, 2, zyaada aam value hai.

3. Rintu ke khajoor ke ped. 29 lambaaiyon ka jod 1621 ft hai, isliye mean 1621 ÷ 29 ≈ 55.9 ft hai. Sort karne pe 15vi value 56 ft hai, yaani median. Ped 43 se 67 ft ke hain, zyaadatar 50 aur 62 ft ke beech, aur chaar theek 60 ft ke. Mean aur median lagbhag barabar hain, isliye koi bada outlier nahi. Mean nikaalne ka tez tareeka: har lambaai se 50 ghatao, farkon ko jodo (171), 29 se bhaag do (lagbhag 5.9) aur 50 waapas jodo. Barabar values ko group karna, jaise 60 × 4, bhi samay bachaata hai. 13 ped mean se chhote hain: 43, 44, 45, 46, 49, 50, 51, 52, 52, 54, 54, 55 aur 55 ft.

4. Roz paani ka istemaal. (a) Nahi. Har value 3.09 L aur 20.5 L ke beech hai. Mean (87.39 ÷ 9 ≈ 9.71 L) aur median (8 L, sort ki hui values mein paanchvi) is daayre ke andar hi honge, isliye koi bhi 25 se 30 L ke beech nahi ho sakta. (b) Nahi. Mean oonchi aur neechi values ko unke beech ki ek value pe barabar karta hai, aur median sort kiye data ki beech waali value hai, isliye dono hamesha minimum aur maximum ke beech rehte hain. Wo minimum ke barabar tabhi ho sakte hain jab saari values barabar hon.

5. Navjaat bachchon ka wazan. Ladke: 2.6 se 4.1 kg, mean 20.6 ÷ 6 ≈ 3.43 kg, median (3.4 + 3.5) ÷ 2 = 3.45 kg. Ladkiyan: 2.5 se 4.0 kg, mean 20.1 ÷ 6 = 3.35 kg, median (3.4 + 3.4) ÷ 2 = 3.4 kg. Dono groups 1.5 kg mein phaile hain aur 3 aur 4 kg ke beech ikatthe hain. Yahan ladke average mein thode bhaari hain, par har group mein chhe bachche itne kam hain ki isse aam nateeja nahi nikaal sakte.

6. Ek aur Grade 5 section. Ladkon ki lambaai lagbhag 130 se 148 cm hai aur 143–146 cm ke aas paas ikatthi hai (mean 142.05, median 143). Ladkiyon ki lambaai zyaada phaili hai, lagbhag 126 se 158 cm (mean 140.14, median 140). Poori class ka mean 141.21 cm aur median 142.5 cm hai. Is section mein ladke average mein lambe hain, jabki pehle section mein ladkiyan thi (142.94 ke mukaable 146.9). Dono sections ki tulna: pehla section kul milaakar lamba hai (mean 141.21 ke mukaable 144.4 cm, median 142.5 ke mukaable 145 cm). Ek hi school ki do classes mein ladkon aur ladkiyon ka nateeja palat jaata hai, isliye ek class se ye nahi keh sakte ki aam taur pe ladke lambe hain ya ladkiyan.

7. Sumo pahalwaan aur ballet dancer. Sumo pahalwaan: 1201.9 ÷ 5 ≈ 240.4 kg. Ballet dancer: 254.5 ÷ 6 ≈ 42.4 kg. 240.4 ÷ 42.4 ≈ 5.7 hai, isliye ek sumo pahalwaan ballet dancer se lagbhag 6 guna bhaari hai.

Data ki tasveer (pages 114–115)

Kya table graph se milti hai? Haan. Har jodi ke bars table se milte hain, jaise January mein 25 aur 19, aur June mein dono shehron ke 35.

Scale kya hai? 1 unit = ₹10.

Kya mahine waar daam compare karna aasaan hai? Haan. Har mahine ke dono daam bagal bagal mein khade hain, isliye lamba bar turant mehenga shehar dikha deta hai.

Take off! (pages 115–118)

Tumhare observations, aur desh. SpaceX aur United Launch Alliance USA ki hain; Rocket Lab USA ki company hai jo zyaadatar New Zealand se launch karti hai. CASC, Galactic Energy aur Expace China ki hain, Roscosmos Russia ki, Arianespace France (Europe) ki aur ISRO India ki. SpaceX sabse zyaada launch karti hai aur sabse tez badhti hai.

Kaunse statements sahi thehraaye ja sakte hain? Values 1 unit = 20 rocket se padhi gayi hain, isliye andaaze hain.

• (a) Nahi. Arianespace ne har saal kam launch kiye, aur United Launch Alliance ne 2023 mein kam.
• (b) Haan. Sirf SpaceX, jo USA ki hai, 50 paar karti hai (2022 mein lagbhag 61 aur 2023 mein 96); CASC ka sabse zyaada lagbhag 48 hai.
• (c) Haan. Arianespace ne lagbhag 15 + 6 + 3 = 24 launch kiye, jo 40 se kam hai.
• (d) Haan. CASC ne lagbhag 48, 35 aur 45 launch kiye, mean lagbhag 128 ÷ 3 ≈ 43, yaani 40 ke aas paas.
• (e) Haan. ISRO ne lagbhag 2 + 5 + 7 = 14, Galactic Energy ne lagbhag 1 + 2 + 7 = 10.
• (f) Nahi. Roscosmos ne lagbhag 16 + 21 + 18 = 55 launch kiye, jo 60 se kam hai.

Kin sansthaon ne har saal zyaada rocket launch kiye? SpaceX, ISRO aur Galactic Energy. Rocket Lab aur Expace 2021 se 2022 mein barabar rahe aur phir badhe.

2023 mein kul launch. Lagbhag 96 + 45 + 18 + 3 + 9 + 3 + 7 + 7 + 6 + 26 ≈ 220, isliye (b) 200 se 400.

Tum kya jaanna chahte ho? Khule sawaal, jaise: USA itne rocket kyun launch karta hai? Rockets kya le gaye? 2024 mein kya hua?

Ek hi samay garmi aur sardi (pages 118–121)

Data kis baare mein ho sakta hai? Har mahine daylight ke ghante. City 1 ko sabse zyaada June mein milta hai aur City 2 ko December mein, jo ulte hemispheres ki taraf ishaara karta hai: City 1 Helsinki hai aur City 2 Wellington.

Math Talk: aur kya explore karna chahoge? Jaise dhruvon ke paas midnight sun, saal bhar mein tumhare apne shehar ki daylight kaise badalti hai, ya Equator ke paas ki jagahon ko saal bhar lagbhag 12 ghante daylight kyun milti hai (Extra).

Ek minute ki baat (pages 121–122)

1. Pehle batting kisne ki? Match kisne jeeta? Neeli innings poore 20 over chalti hai, jabki laal innings bina wicket khoye 18 over pe ruk jaati hai. Doosri batting karne waali team target paar karte hi ruk jaati hai, isliye aam padhaai ye hai ki neeli team ne pehle batting ki aur laal team ne chase karke jeeta. Par bars jaise bane hain unhe jodne pe neeli team ke lagbhag 163 run aate hain aur laal ke sirf lagbhag 152, jo target paar nahi karte. Isliye sirf graph se ye tay nahi hota ki kaun jeeta; shaayad match chhota kiya gaya, jaise baarish se.

2. Over 12 mein neeli team ke run. 15 run.

3. Laal team ke sabse kam run. Over 4, lagbhag 2 run.

4. Kya target batana aasaan hai? Nahi. Graph har over ke run dikhata hai, total nahi, isliye saare 20 neele bars jodne padte hain: lagbhag 163 run, to target 164 hota.

Figure it Out (pages 122–125)

1. Jaanwaron ki raftaar. Haan, ye bar graph hai: har jaanwar ka ek hi chaudaai ka bar hai jiski lambaai ek common scale pe uski top speed dikhati hai, aur rang hawa, zameen aur paani batate hain. (a) Scale ek gridline = 16 kph hai, lagbhag 10 miles per hour. (b) Khula: jaise peregrine falcon ka 322 kph ka gota, ya 8 kph pe andha bhaagta tiger beetle. (c) Jodiyan jahan ek doosre ka lagbhag dugna hai: sailfish (109 kph) aur flying fish (56 kph), spine-tailed swift (170) aur pronghorn antelope (88), aur peregrine falcon (322) aur swift (170). (d) 109 ÷ 26 ≈ 4.2, isliye haan, sailfish humpback whale se lagbhag 4 guna tez hai. Nahi, hum sailfish ko duniya ka sabse tez paani ka jaanwar nahi keh sakte: graph mein sirf paanch paani ke jaanwar hain.

2. Superpower survey. Akshar ginne pe (har grade mein 25 students):

Pasand	Grade 5, Grade 9
Aerial (a)	13, 8
Aquatic (w)	6, 6
Spaceborne (s)	2, 9
Koi nahi (n)	4, 2

1 unit = 2 students ke saath, Grade 5 ki pasand aerial hai aur Grade 9 ki spaceborne, aquatic dono mein barabar hai, aur Grade 9 mein kam students ne koi nahi chuna.

3. Jodhpur ka taapmaan. 1 unit = 4 °C ke saath, Day 1 16 se 34 °C tak aur Day 2 30 se 43 °C tak hai; dono subah 6 baje ke aas paas sabse thande aur dopahar 3 baje ke aas paas sabse garam hain. Thandi subah aur garam dopahar waala Day 1 March (ya November) ka ho sakta hai. Dopahar mein 40 °C se upar waala Day 2 shaayad May ya June ka hai, Jodhpur ke sabse garam mahine.

4. Electric vehicles. (a) Gujarat ke bars 69,000, 89,000 aur 78,000 tak, aur Delhi ke 74,000, 81,000 aur 62,000 tak jaate hain, jaise neeche ke graph mein. (b) Rajya horizontal line pe hain, har ek ke 2022, 2023 aur 2024 ke teen alag rang ke bars, aur scale 1 unit = 25,000 gaadiyan hai. (c) Uttarakhand dheere badha; West Bengal, Andhra Pradesh, Odisha aur Assam har saal badhe, West Bengal sabse tez; Gujarat 2023 mein badha aur 2024 mein ghata; Delhi 2023 mein badha aur 2024 mein tezi se ghata. (d) Assam: lagbhag 60,000 − 40,000 = 20,000 zyaada. (e) West Bengal: 2022 mein lagbhag 10,000 se 2024 mein 43,000, lagbhag 4 guna. (f) Nahi. Har bar us saal register hui gaadiyon ki ginti hai, chalta hua total nahi. Uttarakhand mein 2023 mein lagbhag 16,000 aur 2024 mein 19,000 gaadiyan register hui, jo kam nahi; bar ki lambaai mein chhota badlaav sirf ye batata hai ki har saal ki ginti lagbhag ek jaisi rahi.

Data detective (pages 125–129)

Telling tall tales: tumhe kya dikhta hai? Dot plots mein mean lambaai ye hai:

Grade aur school	Ladke, ladkiyan (cm)
Grade 6, School A	134.8, 137.78
Grade 6, School B	149.84, 150.2
Grade 7, School A	141.8, 141.83
Grade 7, School B	156.14, 155.41
Grade 8, School A	149.35, 147.81
Grade 8, School B	156.14, 156.83

School B ke students har grade mein School A se 7 se 15 cm lambe hain. School A mein lambaai grade dar grade badhti hai, jabki School B ke Grade 7 aur Grade 8 ke ladkon ke plot bilkul ek jaise hain (dono ka mean 156.14), jo do baar chhapa hua plot lagta hai. Ek hi grade ke ladke aur ladkiyan paas paas hain, kabhi ek aage aur kabhi doosra.

Table se kaunse statements sahi thehraaye ja sakte hain?

1. Haan, 1989 ko 2019 se compare karke: har umar pe ladke aur ladkiyan dono 2019 mein lambe the. Har dashak mein aisa nahi hua; kuch umron mein 1989 se 1999 tak 0.1–0.2 cm ki kami aayi.
2. Nahi. 1989 mein 13 saal ki ladkiyon ka average 143.2 cm tha, jo 2009 mein 14 saal ki ladkiyon ke 148 cm se kam hai.
3. Haan, bas thoda sa: 2019 mein 15 saal ke ladkon ka average 159 cm tha, 1989 mein 16 saal ke ladkon ke 158.9 cm ke mukaable.
4. Sahi nahi thehraaya ja sakta. Table average deti hai, jo har ek ladki ke baare mein kuch nahi batata.
5. Nahi. 11 aur 12 saal ki umar pe har survey ke saal mein ladkiyan average mein lambi hain, jaise 2019 mein 11 saal pe 137 cm ke mukaable 138.6 cm.
6. Sahi nahi thehraaya ja sakta. Table 19 pe ruk jaati hai. 2019 mein ladke 18 se 19 ke beech sirf 0.5 cm badhe, yaani badhna dheema ho raha hai.

2019 mein bachche sabse zyaada kab badhe? Ladke 12 aur 13 saal ke beech, 142.2 se 148.4 cm (6.2 cm). Ladkiyan 10 aur 11 saal ke beech, 132.8 se 138.6 cm (5.8 cm).

Navjaat 50 cm ke hon to 1 se 4 saal ki lambaai ka andaaza. 2019 mein paanch saal ke bachche lagbhag 107 cm ke the, isliye 50 cm se ek saman chadhaai har saal lagbhag (107 − 50) ÷ 5 ≈ 11.4 cm jodti hai: 1, 2, 3 aur 4 saal pe lagbhag 61, 73, 84 aur 96 cm. (Extra: bachche pehle saal mein sabse tez badhte hain, isliye asli average 75, 86, 95 aur 102 cm ke kareeb hote hain.)

2029 ki lambaai ka andaaza. Maan lo har umar 2019 se 2029 tak utni hi badhti hai jitni 2009 se 2019 tak, yaani 2019 ki value mein 2009 se 2019 ka badlaav jodo:

Umar	2029 mein ladke, ladkiyan (cm)
5	109.1, 110.4
6	115.2, 116.1
7	121.0, 121.2
8	126.1, 125.8
9	131.0, 130.7
10	135.8, 135.7
11	140.3, 141.5
12	145.5, 146.5
13	151.6, 150.3
14	157.3, 152.8
15	161.7, 154.7
16	164.7, 156.0
17	166.6, 156.8
18	167.7, 157.4
19	167.9, 157.4

Deshon waala graph kaise bana hai? Tumhe kya dilchasp laga? Desh neeche sabse chhote, Timor-Leste, se sabse lambe, Netherlands, tak chalte hain. Har desh ke chaar nishaan hain: 1989 aur 2019 mein ladke (×) aur ladkiyan (▲). Vertical line 145 cm se shuru hoti hai, jo farkon ko zoom karke dikhati hai. Zyaadatar deshon mein 2019 ke nishaan 1989 waalon se upar hain, har jagah ladke ladkiyon se lagbhag 10 se 15 cm lambe hain, aur India ke 19 saal ke yuva dikhaaye gaye chhote groups mein hain.

A mean decision. Parivaar ki average lambaai pe bana darwaaza lambe logon ke liye neecha padega. Darwaaza sabse lambe insaan ke hisaab se banna chahiye, yaani yahan average galat number hai.

Figure it Out (pages 129–134)

1. Jebein. Ladke (12 bachche): 3 jeb (1), 4 (4), 5 (5), 6 (2), isliye mean 56 ÷ 12 ≈ 4.67, median 5 aur range 3 se 6. Ladkiyan (13 bachche): 0 (1), 2 (1), 3 (4), 4 (5), 5 (1), 6 (1), isliye mean 45 ÷ 13 ≈ 3.46, median 4 aur range 0 se 6. (a) Galat: ladkiyon ka data zyaada badalta hai. (b) Sahi: 5 > 4. (c) Galat: 3.46 < 4.67. (d) Galat: dono ka maximum 6 hai. Sirf (b) sahi hai.

2. Har game ke points. (a) A: (14 + 16 + 10 + 10) ÷ 4 = 12.5 points. (b) C ke total ko 3 se bhaag do, kyunki C ne ek game nahi khela: (8 + 11 + 13) ÷ 3 ≈ 10.67. B ke total ko 4 se bhaag do, kyunki B ne chaaron game khele aur 0 asli score hai: 18 ÷ 4 = 4.5. (c) A ne sabse mazboot pradarshan kiya, sabse ooncha mean aur tikau score.

3. General knowledge quiz. Pehla group (10 students): jod 730, mean 73, median (76 + 81) ÷ 2 = 78.5, range 39 se 95. Doosra group (9 students): jod 681, mean ≈ 75.67, median 79, range 47 se 93. Doosre group ne dono maapon pe thoda behtar kiya. Pehle group mein 39 aur 48 jaise kam score mean ko median se kaafi neeche kheench lete hain.

4. Pasandida khel. 1 unit = 200 log ke saath, double bar graph dikhata hai ki har khel ko khelne se zyaada log dekhte hain. Cricket sabse zyaada dekha (1240) aur sabse zyaada khela (620, dekhne waalon ka theek aadha) jaata hai, athletics dono mein sabse kam, aur basketball aur swimming khelne waalon ki ginti barabar hai (320).

5. 17 students ko do barabar groups mein baantna. Sort karne pe: 101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125. Median use karo: 115 cm pe khada 9va student baantne waali lambaai hai. Usse pehle ke 8 students chhota group aur baad ke 8 lamba group banaate hain, aur median waala student beech mein rehta hai. Paanch students 115 cm ke hain, isliye unka kram tay karne ke liye unhe millimetre tak naapo. Mean lambaai 1930 ÷ 17 ≈ 113.5 cm hai. 2019 ki table mein 6 saal ke bachche lagbhag 113 cm aur 7 saal ke lagbhag 118 cm ke hain, isliye ye students shaayad lagbhag 6 saal ke hain.

6. Tumhari apni class. Sabko naapo, lambaai sort karo, mean aur median nikaalo, dot plot banaao, aur sabse chhota, sabse lamba aur lambaai kahan ikatthi hai ye batao.

7. Do sections. (d): ek section ki mean lambaai doosre section ke mean ke baare mein kuch nahi batati.

8. Toofaan mein oonche khade. (a) Label waale bars ko dekhkar (Hong Kong 553, Shenzhen 367, Dubai 251): New York lagbhag 315, Tokyo lagbhag 165, London lagbhag 30 skyscrapers. (b) (i) Sahi. Chart sabse zyaada skyscrapers waale shehar dikhata hai, aur unme se 12 ke paas Mumbai ke 86 se zyaada hain; chart se baahar ke kisi bhi shehar ke paas London se bhi kam hain. (ii) Sahi nahi. Chart pe sirf 7 shehron ke paas Mumbai se kam hain, par duniya ke har us shehar ke paas bhi kam hain jo chart pe nahi hai. (iii) Sahi nahi. Chart har shehar mein 150 m se oonchi imaaraton ki ginti dikhata hai; ye nahi dikhata ki sabse oonchi akeli imaarat kaunsi hai. (Extra: sabse oonchi imaarat, Burj Khalifa, Dubai mein hai.)

9. Pehle andaaza, phir naap. Har cheez ke liye andaaza likho, phir naapo aur positive fark nikaalo. Jaise 15, 5, 17, 18 aur 25 cm ke andaaze aur 14.2, 4.4, 18.1, 17.5 aur 27.9 cm ke naap se fark 0.8, 0.6, 1.1, 0.5 aur 2.9 cm aate hain, average fark 5.9 ÷ 5 = 1.18 cm. Har cheez ke andaaze aur naap ko bagal bagal rakhkar double bar graph banaao.

10. Aditi ke Sudoku time. Week 1 (9 puzzles): mean 3240 ÷ 9 = 360 s, median 360 s, range 310 se 410 s. Week 2 (8 puzzles): mean 2230 ÷ 8 = 278.75 s, median (270 + 280) ÷ 2 = 275 s, range 220 se 380 s. Wo tez ho gayi: Week 2 ke aath mein se chhe time Week 1 ke har time se kam hain. Week 2 ka 380 s asaamaanya roop se dheema hai, shaayad mushkil puzzle tha, aur ye Week 2 ke mean ko median se upar utha deta hai.

11 se 13. Projects. Inke liye tumhara apna data chahiye. Har project mein data dhyaan se ikattha karo, minimum, maximum, mean aur median nikaalo, dot plot ya double bar graph banaao, aur do teen observations likho. Naamon waale project mein median shuruaati akshar batata hai ki zyaada naam A se M se shuru hote hain ya N se Z se. Ek minute aur teen minute ke andaazon mein har parivaar ke mean ko 60 s aur 180 s se compare karo.

Puzzle time: connect the dots (page 135)

Number lock. Code 415 hai. 036 se pata chalta hai ki 0, 3 aur 6 code mein nahi hain. 064 se 4 code mein hai par teesra nahi, aur 542 se doosra bhi nahi, isliye 4 pehla hai. 265 mein ek digit sahi aur sahi jagah pe hai; 2 pehla nahi ho sakta, isliye 5 teesra hai. Isse 542 ke do sahi digit 4 aur 5 ban jaate hain, isliye 2 code mein nahi. 271 mein ek digit sahi hai par galat jagah pe: beech mein 7 sahi jagah pe hota, isliye wo digit 1 hai, aur wo beech mein jaata hai.