MathsPushan · Class 9-10
Histogram: jab data bahut ho, toh varg banao
Akhbaar ke ek paragraph ke 50 shabdon mein har shabd kitne akshar ka hai — yeh 50 alag number ek nazar mein kaise samjhoge?
Socho pehle… phir dekho jawab
Unhe vargon (classes) mein baanto — 1-3 akshar, 4-6, 7-9 — aur har varg ki frequency gino. Phir histogram banao: khambe aapas mein chipke hue, kyunki varg lagaatar hain. Data ka 'aakaar' turant dikh jaata hai.
Ishaan ko school ke health camp mein 40 bachchon ki lambai ki list mili. Sab chahte the ki woh bas 'average' bata de. Ishaan ne tay kiya ki pehle poora aakaar dekhega — kahin kuch bachche bahut alag toh nahi, jinhe doctor ko dobara dekhna chahiye?
Grouped data: jab data bahut ho, barabar chaudai ke varg banate hain, jaise 130-135, 135-140 cm. Niyam: 135 cm wala bachcha 135-140 mein gina jaata hai (upper limit agle varg mein). Har varg mein kitne aaye, woh uski frequency hai.
Histogram vs bar graph: bar graph alag-alag cheezon (cricket, kabaddi) ke liye hai, khambon ke beech gap hota hai. Histogram lagaatar data (lambai, umar, varsha) ke liye hai; khambe chipke hote hain aur chaudai varg ka size hai. Agar vargon ki chaudai barabar na ho, toh oonchai frequency ko chaudai ke anupaat mein sudhaar kar banani padti hai — warna bada varg jhootha ooncha dikhega.
Yeh kahan chhupa hai? Aabaadi ka umar-wala chitra (population pyramid), varsha ke aankde, aur 1950 mein P.C. Mahalanobis ki pahal se shuru hua National Sample Survey — sab grouped data se desh ko samajhte hain. Aage yahi grouped mean, median aur Class 11 ka 'spread' (standard deviation) banta hai.
Ghar pe try karo
Akhbaar ka koi paragraph lo aur pehle 50 shabdon ke akshar gino. Varg banao: 1-3, 4-6, 7-9, 10-12. Frequency table bharo, phir copy mein histogram banao (khambe chipke hue). Kaun sa varg sabse ooncha aaya, aur kyun ho sakta hai?
Wow!
'Average' poore data ko ek number mein dabaa deta hai; histogram uski poori shakal dikhata hai — kabhi-kabhi do pahad wali shakal bhi!
3 sawaal
- Histogram mein khambe aapas mein chipke kyun hote hain?
Jawab dekho
Kyunki data lagaatar (continuous) vargon mein hai. Varg ek ke baad ek lagaatar hain, isliye khambon ke beech gap nahi.
- Varg 130-135 aur 135-140 hain. 135 cm wala bachcha kis varg mein jaayega?
Jawab dekho
135-140. Upper limit apne varg mein nahi, agle varg mein gini jaati hai.
- Vargon ki chaudai barabar na ho toh histogram mein kya karna chahiye?
Jawab dekho
Oonchai ko chaudai ke anupaat mein sudhaarna. Warna chauda varg zyada frequency ka jhootha aabhaas deta hai.
NCERT se jodo: NCERT Class 9 Maths — statistics: grouped frequency distribution aur histogram