Empirical Rule Calculator (68-95-99.7 Rule)

Your details

The arithmetic average of your dataset. For a standard normal distribution this is 0.
A measure of spread: how far typical values stray from the mean. Must be greater than zero.
Any single value from your dataset. The calculator will find its z-score and which sigma band it falls in.
Z-score of your valueWithin 1 SD of mean
1

How many standard deviations your observed value is from the mean

1σ lower bound85
1σ upper bound115
2σ lower bound70
2σ upper bound130
3σ lower bound55
3σ upper bound145
Sigma bandWithin 1σ (68% band)
Approximate percentile84.13%
68% interval85 to 115
95% interval70 to 130
99.7% interval55 to 145
184.1% below · Standard deviations from mean

With mean 100 and SD 15, the central 68% interval spans 85.00 to 115.00.

  • About 68% of your data falls between 85 and 115 (within 1 standard deviation).
  • About 95% of your data falls between 70 and 130 (within 2 standard deviations).
  • About 99.7% of your data falls between 55 and 145 (within 3 standard deviations). Only 0.3% lies outside this range.
  • Your observed value of 115 has a z-score of 1.00: it is within 1σ (68% band). Approximately 84.1% of the distribution lies below it.

Next stepThe empirical rule applies only when data are approximately normally distributed. Check a histogram or Q-Q plot first to confirm normality before using these intervals.

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