How to find the 80th percentile with mean and standard deviation
The Correct Answer and Explanation is:
To find the 80th percentile of a normally distributed dataset using only the mean and standard deviation, apply the following approach:
✅ Correct Answer:
Use the formula P = μ + zσ where
- P is the percentile value
- μ is the mean
- σ is the standard deviation
- z is the z-score corresponding to the desired percentile
For the 80th percentile, the z-score is approximately 0.8416. Thus, the 80th percentile is: P = μ + 0.8416 × σ
📘 Explanation
Percentiles indicate the relative standing of a value within a dataset. The 80th percentile marks the point below which 80 percent of the data lies. In the context of a normal distribution, values are symmetrically distributed around the mean, with the spread controlled by the standard deviation.
To calculate a percentile, we must first identify the corresponding z-score. The z-score represents the number of standard deviations a value is from the mean. For the 80th percentile, statistical tables or software tools show that the z-score is approximately 0.8416. This means the 80th percentile lies 0.8416 standard deviations above the mean.
The general formula for converting a z-score into an actual value is P = μ + zσ. This transforms the relative position (z) into an absolute value (P), using the dataset’s mean and spread. Plugging in the values: P = μ + 0.8416 × σ, we get a precise estimate of the 80th percentile.
For example, if a dataset has a mean of 100 and a standard deviation of 15, then: P = 100 + 0.8416 × 15 = 112.624
This result means that 80 percent of values in the dataset are less than approximately 112.624.
This method assumes the data follows a normal distribution. If the dataset is skewed or has outliers, then a percentile based on z-scores may be misleading. In such cases, non-parametric methods are preferred.
