1.1.5 · D5 · HinglishMeasurement, Vectors & Kinematics
Question bank — Errors — absolute, relative, percentage; systematic vs random
1.1.5 · D5· Physics › Measurement, Vectors & Kinematics › Errors — absolute, relative, percentage; systematic vs rando
Do words jinhe hum baar baar use karenge — pehle inhe theek se samajh lo taaki neeche koi line inhe "bina kamaaye" use na kare:
Koi bhi symbol use karne se pehle, yahan exact quantities hain jinhe trap kiya jayega. Neeche kuch bhi appear nahi ho sakta jab tak wo is list mein na ho.
True or false — justify karo
Neeche har statement ya toh true hai ya false. Bolo kaun sa, phir reason do — sirf "true/false" kuch score nahin karta.
Zyaada readings lene se systematic error eventually remove ho sakti hai.
False. Systematic error har reading par same nudge hai (e.g. hamesha cm), toh sum karke divide karne par wahi cm peeche reh jaata hai. Sirf random scatter averaging se shrink hoti hai.
Ek precise measurement automatically accurate bhi hoti hai.
False. Precise readings tightly clustered hoti hain lekin poora cluster true value se bahut dur ho sakta hai (ek systematic bias). Tum "precisely wrong" ho sakte ho.
Relative error ka unit measured quantity ke jaisa hi hota hai.
False. Relative error hai — upar aur neeche ke units cancel ho jaate hain, toh ye dimensionless hai. Isi liye ye tumhe ek length error ko ek mass error se compare karne deta hai.
Absolute error negative ho sakta hai.
False. Ye modulus ke saath define hota hai, , toh ye ek magnitude hai — miss ka size, kabhi uski direction nahin.
Ek instrument par zero error ek random error hai.
False. Zero error ka matlab hai instrument zero input par ek fixed non-zero amount read karta hai, toh ye har reading ko identically offset karta hai — ye systematic error ki textbook signature hai.
Percentage error aur relative error mein same information hoti hai.
True. Percentage error sirf relative error hai; ek constant se multiply karna insani aankhon ke liye number ko reshape karta hai lekin koi nayi information add nahin karta.
Kisi data set ka mean absolute error aur standard deviation hamesha equal hote hain.
False. Dono spread measure karte hain lekin alag recipes se — MAE ko average karta hai, jabki unhe root-mean-square karta hai, toh generally bada hota hai. Dono ek hi sawaal ka jawab outliers ke liye alag sensitivity ke saath dete hain.
Readings ki sankhya double karne se mean ki uncertainty half ho jaati hai.
False. Standard error ki tarah girta hai, toh double karne par uncertainty sirf se divide hoti hai; half karne ke liye tumhe chaar guni readings chahiye — aur tab bhi sirf random error shrink hoti hai.
Agar do students ek hi rod measure karein aur unka mean same aaye, toh unki uncertainty bhi same hogi.
False. Equal means mein bahut alag scatter chupi ho sakti hai; jis ke readings widely spread hain uska mean absolute error bada hai, isliye uska range bada hai.
error wali measurement hamesha error wali se zyaada trustworthy hoti hai.
Accuracy ke liye False. Chhoti percentage error sirf tight, consistent readings reflect karti hai; ek unnoticed systematic bias "" result ko confidently galat bana sakti hai. Chhoti relative error matlab precise hai, accurate necessarily nahin.
Galti dhundho
Har line mein reasoning ya reporting mein ek specific galti hai. Usse naam do aur correct karo.
"Maine ek wire mm measure ki — dekho meri error kitni precise hai."
Error bahut zyaada significant figures mein stated hai; uncertainty khud uncertain hoti hai, toh use 1 (kabhi kabhi 2) sig figs mein round karo aur value ke decimals se match karo: mm.
"Meri readings g hain, toh mera result perfectly accurate hai."
Tight readings precision prove karti hain, accuracy nahin. Agar balance mein g zero error tha, toh teeno equally offset hain aur true mass g hai — sirf spread se accuracy judge nahin kar sakte.
"Error mm hai aur length m hai, toh ye ek buri measurement hai."
Sirf absolute error se quality judge karna galti hai. Relative error hai — excellent. Wahi mm ek mm wire par hoga, terrible. Miss ka size cheez ke size ke against weigh karna padta hai.
"Maine apni kaanpte haath wali readings average kari, toh maine apni random aur systematic dono errors fix kar di."
Averaging sirf random scatter ko cancel karta hai. Koi bhi systematic bias (parallax hamesha ek taraf jhukna, ek mis-calibrated scale) average ke through seedha nikal jaati hai untouched.
"Percentage error hamesha hai, bas."
Dhyan do — denominator matter karta hai. Strictly, percentage error us value se divide karta hai jise tum reference maante ho: measured/mean value (fractional uncertainty, jo school work use karta hai) ya true/accepted value (jab kisi known standard se compare kar rahe ho). Dono tabhi agree karte hain jab measurement truth ke karib ho; batao tum kaun sa use kar rahe ho.
"Mera percentage error hai kyunki maine jo digits padhe wo bahut chhote the jaise ."
Percentage fraction par depend karta hai, reading ke digits kitne chhote hain is par nahin. Chhote numbers ka matlab automatically bada percentage error nahin hota — guess karne se pehle ratio compute karo.
"Mujhe g ka ek systematic error mila, toh main use hatane ke liye zyaada readings lunga."
Galat tool. Jab ek systematic error identify aur quantify ho jaata hai, to tum use repetition se nahin balki subtraction se correct karte ho — har reading se g ghata do.
Why questions
Ye mechanism probe karte hain. Reasoning ke bina sahi final phrase incomplete hai.
Averaging random error kyun reduce karta hai lekin systematic error kyun nahin?
Random errors coin-flip nudges ki tarah hain, kabhi kabhi , toh sum mein partly cancel ho jaate hain; systematic error har baar identical nudge hai, toh copies sum karke se divide karne par wahi nudge wapas aata hai. Figure s02 ke do clouds ye seedha dikhate hain.
Mean ki uncertainty ki tarah kyun girti hai, ki tarah nahin?
Kyunki random deviations partly cancel hote hain fully nahin — ye ek random walk ki tarah add hote hain, jiska typical size ki tarah badhta hai, toh summed error ko se divide karne par shrinkage milti hai. Dekho Mean and Standard Deviation.
Hum mean ko true value ka best estimate kyun maante hain?
Kyunki random errors symmetrically truth ke aas paas scatter hote hain, woh value jo total squared deviation minimize karta hai woh arithmetic mean hai — ye woh single number hai jis ki taraf "highs aur lows cancel hote hain."
Relative error nikalne ke liye hum value se divide kyun karte hain, sirf absolute error kyun nahin quote karte?
Ek fixed absolute error alag alag scales par wildly alag cheezein matlab rakhta hai; value se divide karne par miss cheez ke ek fraction ke roop mein express hota hai, jo alag quantities ke errors ko directly comparable aur unit-free banata hai.
Har reading ki error compute karte waqt hum absolute value (modulus) kyun use karte hain?
Hum deviation ka magnitude chahte hain. Modulus ke bina, positive aur negative deviations cancel ho jaate aur mean deviation zero ki taraf collapse ho jaata, real spread chupaate hue.
Ek jaana-pehchana systematic error actually deal karne mein aasaan kyun hota hai, averaging fail hone ke bawajood?
Kyunki ye constant aur predictable hai — ek baar offset measure ho jaane ke baad (e.g. zero reading), tum use exactly subtract karte ho. Random error mein subtract karne ke liye koi fixed value nahin hoti, sirf ek spread hoti hai jo statistically shrink hoti hai.
Reported uncertainty value ke last decimal place se kyun match karni chahiye?
Kyunki value ko apni uncertainty se zyaada decimals tak claim karna aisi knowledge claim karna hai jo tumhare paas hai nahin; value sirf us digit tak meaningful hai jahan error bite karta hai. Dekho Significant Figures and Rounding.
Edge cases
Boundary aur degenerate situations jo definitions ko phir bhi handle karni padti hain.
Agar saare readings identical hain, toh mean absolute error kya hai?
Bilkul zero — mean se har deviation zero hai. Lekin reported zero error ka matlab zero true error nahin; ek chupi systematic bias ya instrument ki least count real accuracy ko ab bhi limit karti hai.
Tum sirf ek reading lete ho. Kya mean absolute error compute ho sakta hai?
Nahin — ek reading ke saath mean us reading ke equal hota hai aur uska deviation zero hai, jo ek meaningless "zero" uncertainty deta hai. Honest uncertainty phir instrument ki least count se aani chahiye (dekho Least Count and Vernier Calipers), scatter se nahin.
Tum apni current uncertainty half karna chahte ho. Roughly kitni aur readings chahiye?
Total mein roughly chaar guni, kyunki standard error ki tarah scale karta hai — aur ye tab hi kaam karta hai jab dominant error random ho; koi systematic bias kitni bhi readings lo, nahin badlegi.
Tumhara mean absolute error mean value se bada nikla (relative error ). Ye kya signal karta hai?
Measurement essentially useless hai — scatter signal ko dabaata hai. Iska matlab usually blunder, galat instrument, ya koi quantity itni zero ke paas hai ki fraction blow up kar jaaye.
Measured mean exactly zero hai (e.g. net force reading). Relative error ka kya hoga?
Ye undefined hai — zero se divide nahin kar sakte. Zero true value ke paas, relative aur percentage error ka matlab nahin rehta, toh tumhe absolute error report karni chahiye.
Ek reading jo wild outlier hai (ek clear mistake, jaise ruler slip ho gaya) tumhare data set mein hai. Kya ye random error hai?
Nahin — ek genuine blunder ya mistake statistical sense mein na random hai na systematic; use analysis se pehle discard karna chahiye, mean mein fold nahin karna, jahan wo mean aur mean absolute error dono ko distort kar dega.
Dono students average par true value hit karte hain, lekin ek ne ek biased instrument use kiya jo ittifaq se cancel ho gaya. Kya woh instrument accurate hai?
Nahin — accidental cancellation luck hai, accuracy nahin. Us biased instrument ki ek akeli reading phir bhi off hogi; sirf is particular data set ka balance hua. Reliability ke liye bias khud absent hona chahiye.
Recall Jaane se pehle ek-line self-test
Averaging random error fix karta hai, subtraction ek jaane systematic error ko fix karta hai, mean ki uncertainty == ki tarah shrink hoti hai (standard error), aur chhoti relative== (percentage) error ka matlab precise hai lekin necessarily accurate nahin. Agar tum har ek ke liye why bata sako, toh is page ne apna kaam kar diya. Jab tum measurements combine karte ho toh errors kaise propagate karti hain, iske liye jaao Combination of Errors.