Representative value kya hoti hai?

Ek akela number jo numbers ke poore group ki jagah khada ho, taaki groups ko samjhaaya aur compare kiya ja sake. Is chapter mein do representative values hain: mean (average) aur median.

Data ka mean kaise nikalte hain?

Saari values jodo aur jod ko values ki ginti se bhaag do. Paanch dinon mein 2, 7, 9, 4 aur 3 gudhal ke phool khile, to mean (2 + 7 + 9 + 4 + 3) ÷ 5 = 25 ÷ 5 = 5 phool roz hai.

Mean ko barabar hissa kyun kehte hain?

Kyunki total ko barabar baantne pe har ek ko yahi milta. Parag ke 6 logon ke group ne 5, 4, 6, 3, 4 aur 8 amrood ikatthe kiye, kul 30. Barabar baantne pe har ek ko 30 ÷ 6 = 5 milte hain, jo mean hai.

Mean (average) kaise nikalein?

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Kisne behtar batting ki?

Ek cricket series mein Shubman ne 0, 17, 21 aur 90 run banaaye, aur Yashasvi ne 67, 55, 18 aur 35. Kaun behtar raha? Vaishnavi Shubman ke 90 ki taraf ishaara karti hai, sabse bada score. Shreyas run jodta hai: Yashasvi ke 175 aur Shubman ke 128. Phir Vaishnavi dekhti hai ki Yashasvi zyaada tikau tha, kyunki uske sabse bade aur sabse chhote score ka fark kam hai. Har dost numbers ko alag nazar se dekhta hai, aur har nazar kuch sach batati hai.

Agli series mein Shubman ne 23, 7, 10, 52 aur 18 run banaaye, kul 110, jabki Yashasvi ne 26, 53, 2 aur 15 banaaye aur ek match nahi khela, kul 96. Ab total ki tulna theek nahi: Shubman ne paanch match mein batting ki aur Yashasvi ne sirf chaar mein. Hamein ek aisa number chahiye jo har player ki batting ko dikhaaye, ek representative value, jo bade scores ko chhote scores se santulit kare.

Arithmetic mean

Aisa sabse saral number hai arithmetic mean, yaani average:

Mean = saari values ka jod ÷ values ki ginti

Shubman ka mean 110 ÷ 5 = 22 run har match hai aur Yashasvi ka 96 ÷ 4 = 24 run har match, isliye is series mein Yashasvi behtar raha. (Book mein 110 ÷ 5 = 21 chhapa hai; sahi value 22 hai, aur Yashasvi phir bhi aage hai.) Mean ka poora number hona zaroori nahi. Do dhaavak jinke saat time ka jod 122 second hai, dono ka mean 122 ÷ 7 ≈ 17.43 second hai, isliye average mein koi tez nahi.

Mean ek barabar hissa

Mean ek barabar hissa hai

Shreyas aur uske chaar dost 3, 8, 10, 5 aur 4 amrood ikatthe karte hain, kul 30. Parag aur uske paanch dost 5, 4, 6, 3, 4 aur 8 ikatthe karte hain, ye bhi kul 30. Har group barabar baante to Shreyas ke group mein har ek ko 30 ÷ 5 = 6 milte hain aur Parag ke group mein 30 ÷ 6 = 5. Total ek jaisa, hissa alag, kyunki groups ka size alag hai. Socho ki bars ko barabar kiya ja raha hai: lambe bars chhote bars ko dete jaate hain jab tak sab mean pe na aa jaayein. Isi tarah paanch dinon mein 2, 7, 9, 4 aur 3 gudhal ke phool ka mean 25 ÷ 5 = 5 phool roz hai, yaani agar har din ek jaisa hota to roz itne phool khilte.

Bharat ke ganitagyon ne mean ko bilkul isi tarah dekha. Uske naamon mein samarajju (Brahmagupta, 628 CE), samikarana yaani barabar karna (Mahaviracharya, 850 CE), aur samamiti yaani mean maap (Bhaskaracharya, 1150 CE) shaamil hain. Sama ka matlab hai barabar.

Zero ya koi value nahi?

Ek player ke score hain 57, 13, 0, 84, —, 51, 27. 0 ek asli innings hai jisme kuch nahi bana, isliye wo ginti mein aata hai. Dash ka matlab hai ki player ne batting nahi ki, isliye wo match chhod diya jaata hai. Mean (57 + 13 + 0 + 84 + 51 + 27) ÷ 6 = 232 ÷ 6 ≈ 38.67 run har match hai.

Kabhi kabhi zero jaan boojhkar chhode jaate hain. Sita ke aam ke ped ne January se December tak 0, 0, 8, 24, 41, 16, 5, 0, 0, 0, 0 aur 0 aam diye. Mausam mein har mahine ki aam paidaawaar ke liye sirf March se July lo: (8 + 24 + 41 + 16 + 5) ÷ 5 = 94 ÷ 5 = 18.8 aam har mahine. Saare 12 mahinon ka mean, lagbhag 7.8, kisi bhi asli mahine ko nahi dikhata.

Hamare aas paas average

Average har jagah milte hain: kisi mahine mein roz ki average baarish, scooter ka average mileage, kisi rajya mein har hectare gehun ki paidaawaar, ya ek insaan roz kitna kachra phenkta hai. 1500s ki shuruaat mein Europe mein zameen naapne ki rod 16 feet ki tay ki gayi, 16 aadmiyon ko ek ke peechhe ek, ungli se edi milaakar khada karke. Phir rod ke 16 barabar hisse kiye gaye, har ek ek foot, yaani foot solah asli pairon ki average lambaai ban gaya.

Mean pyaaz ka sawaal bhi suljhaata hai. Ek hi baarah mahinon mein Yahapur ke daamon ka jod ₹458 hai aur Wahapur ka ₹450, isliye mean lagbhag ₹38.17 aur ₹37.50 kilo hain: average mein Yahapur mein pyaaz thoda mehenga tha. Par ek number ye nahi dikha sakta ki daam kitna upar neeche hote hain. Uske liye median aur outliers dekho, jahan median aur dot plots aate hain.

Ye kyun zaroori hai

Achhi representative value se groups ki sahi tulna hoti hai, chahe players hon, classes, shehar ya khet. Isi data ko tasveer mein data ko graph mein kaise dikhayein? mein dekho. Textbook ke sawaalon ke jawab Part 2 Chapter 5 ke NCERT solutions mein hain; poore Part 2 Chapter 5 ke notes dekho.