Phần hướng dẫn bên dưới chưa có bằng tiếng Việt nên được hiển thị bằng tiếng Anh. Bản thân máy tính đã được dịch đầy đủ.
Cách sử dụng máy tính này
- Choose what to calculate: a z-score from a raw value, probabilities for a z-score, or the z-score at a percentile.
- Enter the values. The standard deviation must be greater than 0.
- Read the left-tail, right-tail, between and outside probabilities.
Công thức
A z-score counts how many standard deviations a value is from the mean. Probabilities use the standard normal cumulative distribution Φ(z), computed to double precision.
z = (x − μ) / σ
P(Z < z) = Φ(z); P(Z > z) = 1 − Φ(z)
P(−|z| < Z < |z|) = 2Φ(|z|) − 1
Example
- Score 85 on a test with mean 70 and SD 10.
- z = (85 − 70) / 10 = 1.5.
- Φ(1.5) ≈ 0.9332, so the score is at about the 93rd percentile.
Câu hỏi thường gặp
What does a negative z-score mean?
The value is below the mean. A z-score of −1 is one standard deviation below average.
Why is z = 1.96 important?
95% of a normal distribution lies between −1.96 and +1.96 standard deviations, which is why 1.96 appears in 95% confidence intervals.
Does my data need to be normally distributed?
A z-score can be computed for any data, but the probabilities and percentiles only apply if the data are approximately normal.