UPSC Darpan

MathsMarichi · UPSC

Average ke Peeche ka Sach: Spread, Sampling aur Bharat ki Statistical Neev

Kisi State ki 'ausat aay' badh gayi — kya iska matlab hai ki zyadatar logon ki aay badhi? Aur yeh aankda banta kaise hai?

Socho pehle… phir dekho jawab

Mean extremes se kheencha jaata hai; median aur spread (standard deviation, CV, Gini) batate hain ki fayda kitna baraabar baanta. Aur zyadatar sarkari aankde poori ginti nahi, sample survey aur administrative data se bante hain — isliye sample ka design aur bias samajhna GS3 aur CSAT dono ke liye zaroori hai.

Concept: mean, median, mode beech batate hain; range, variance, standard deviation (σ) aur coefficient of variation (CV = σ/mean × 100) phailaav. Do zile jinka ausat ek ho, unme ek mein aay baraabar aur doosre mein kuch logon ke paas kendrit ho sakti hai. Isliye asamanta ke liye Gini coefficient (0 = poori samanta, 1 = poori asamanta) jaise maap use hote hain.

Sampling aur Bharat ki neev: P.C. Mahalanobis ne 1931 mein Kolkata mein Indian Statistical Institute shuru kiya, jise ISI Act, 1959 ne Institute of National Importance banaya; unki pahal se 1950 mein National Sample Survey shuru hua. Achha sample random aur pratinidhi (representative) hota hai — bahut bada sample bhi ek-tarfa ho toh galat nateeja deta hai (selection bias). 29 June, Mahalanobis ki jayanti, Rashtriya Sankhyiki Diwas hai.

CSAT/Prelims traps: (a) har value mein constant jodne se mean badalta hai, σ nahi; (b) har value ko k se guna karne par mean aur σ dono k guna (k positive ho toh); (c) ek bada outlier mean ko kheenchta hai, median ko bahut kam; (d) 'ausat badha' ka matlab 'sabka badha' nahi.

Mains angle (GS3 — growth, inclusion, data governance): achhi neeti achhe data par tikti hai — samay par aankde, paardarshita, base-year revision aur State-star data. Ek paksh: naye administrative aur digital data tez aur saste hain. Doosra paksh: unme coverage aur bias ki seemayein hain, isliye woh sample surveys ki jagah nahi, unke saath chalte hain.

Ghar pe try karo

CSAT-style abhyaas: 5 gharon ki maasik aay (₹ hazaar mein) lo — 10, 12, 14, 16, 98. Mean aur median nikalo; phir 98 ko 18 karke dobara nikalo. Kya badla, kya nahi? Phir 150 shabd likho: 'Ausat aay ka badhna samaveshi vikas ka saboot kyun nahi hai?'

Wow!

Ek outlier (98) ne 5 gharon ki ausat aay 14 se 30 kar di — par median 14 hi raha! Aankda jhooth nahi bolta, par adhoora aankda sach chhupa sakta hai.

3 sawaal

  1. Ek dataset ki har value mein 5 joda jaaye toh kya hoga?
    Jawab dekho

    Mean 5 badhega, σ wahi rahega. Sab values ek saath khisakti hain: kendra badalta hai, phailaav nahi.

  2. Rashtriya Sankhyiki Diwas (29 June) kiski jayanti par manaya jaata hai?
    Jawab dekho

    P.C. Mahalanobis. Indian Statistical Institute ke sansthaapak aur NSS ke prerak P.C. Mahalanobis ki jayanti 29 June hai.

  3. Coefficient of variation ka sahi formula kaun sa hai?
    Jawab dekho

    (σ / mean) × 100. CV spread ko mean ke anupaat mein naapta hai, isliye alag mean wale data ki tulna kar sakta hai.

NCERT se jodo: GS3 — Indian Economy (growth, inclusion, measurement); CSAT — basic numeracy aur data interpretation

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