Z-score Calculator
Value ko z-score mein badlein aur probability nikaalein.
Z-score Calculator poori tarah aapke browser mein chalta hai. Value, mean, standard deviation aur z-scores jo aap daalte hain wo aapki device par hi rehte hain aur kabhi upload nahi hote.
Confidence Interval Calculator kholein
Z-score Calculator ke baare mein
Z-score Calculator kisi value ko z-score mein convert karta hai — yani wo mean se kitne standard deviations door hai — aur turant standard normal distribution se matching probability nikaal deta hai. Value ke saath mean aur standard deviation daalein, ya Raw z-score mode mein switch karke seedha z-score type karein. Ye tool P(X < z) percentile, P(X > z) upper tail, aur significance testing ke liye use hone waala two-tailed p-value deta hai, jo ek accurate erf-based normal curve approximation se calculate hota hai. Ye un students ke liye bana hai jo statistics homework check kar rahe hain, un analysts ke liye jo outliers dhoondh rahe hain, aur kisi bhi aise insaan ke liye jise page chhode bina quick z-table lookup chahiye. Har calculation aapke browser mein locally hoti hai — koi bhi number upload nahi hota.
Features
- Value, mean aur standard deviation ko instantly z-score mein convert karta hai
- Raw z-score mode — jab aapke paas pehle se z ho aur sirf probabilities chahiye
- P(X < z) dikhata hai — percentile ya left-tail probability
- P(X > z) dikhata hai — upper-tail probability
- Significance testing ke liye two-tailed p-value calculate karta hai
- Standard normal CDF ka accurate erf-based approximation
- Z-score aur teeno probabilities ka plain-text summary copy karein
- Zero ya negative standard deviation se guard karta hai
Z-score Calculator kaise use karein
- From value ya Raw z-score mode chunein
- Value, mean aur standard deviation daalein (ya seedha z-score)
- Z-score aur percentile, upper-tail, two-tailed probabilities padhein
- Apni report ya homework ke liye summary copy karein
Example
Input
x=85, μ=70, σ=10
Output
z = 1.5 · P(<z) 0.933
Mean se 1.5 standard deviations upar wali value 93.3rd percentile par hai.
Common errors aur troubleshooting
- Z-score result kuch nahi dikha raha ya error banner aa raha hai. — Standard deviation 0 se zyada hona chahiye — zero ya negative σ se z-score undefined ho jaata hai, isliye positive value daalein.
- P(X < z) aur P(X > z) ka total wo nahi hai jo expect kiya tha. — Definition se ye hamesha 1 hote hain; check karein ki aapko single tail ki jagah two-tailed p-value chahiye ya nahi.
- Negative z-score ke liye percentile reversed lag raha hai. — Negative z ka matlab value mean se neeche hai, isliye P(X < z) sahi tareeke se 50% se kam hoga — ye expected hai, bug nahi.
- Standard deviation ki jagah percentage ya standard error type kar diya. — Z-score Calculator distribution ka raw standard deviation chahta hai, na ki percentage, variance, ya mean ka standard error.
Aksar pooche jaane wale sawaal
- Z-score Calculator asal mein kya calculate karta hai?
- Ye aapki value, mean aur standard deviation se z = (x − μ) / σ calculate karta hai, phir z-table ke erf-based approximation se standard normal distribution par matching probability nikaalta hai.
- Simple bhasha mein z-score kya hota hai?
- Z-score batata hai ki koi value apni distribution ke mean se kitne standard deviations door hai. 1.5 ka z-score matlab value mean se 1.5 standard deviations upar hai.
- P(X < z) aur two-tailed p-value mein kya farak hai?
- P(X < z) percentile hai — us z-score se neeche aane ki probability. Two-tailed p-value chhoti tail ko double kar deta hai aur ye two-sided hypothesis test mein 0.05 jaisi significance threshold se compare hota hai.
- Kya main raw value ki jagah seedha z-score daal sakta hoon?
- Haan. Z-score Calculator ko Raw z-score mode mein switch karein aur z-score type karein — bina mean ya standard deviation daale percentile, upper-tail aur two-tailed probability mil jaayegi.
- Normal distribution probability kitni accurate hai?
- Calculator Abramowitz aur Stegun ka erf approximation use karta hai standard normal CDF ke liye, jo lagbhag 0.00015% tak accurate hai — coursework, QA checks aur real analysis ke liye kaafi hai.
- Kya Z-score Calculator mere numbers upload karta hai?
- Nahi. Har calculation aapke browser mein locally hoti hai. Aap jo values type karte hain wo aapki device se kabhi nahi jaatin aur ArrayKit ko send nahi hoti.
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