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Features of Normal Distribution


9. References

8. Summary

7. Outliers

6. Probability vs. Standard Deviation

5. Normal Distribution Height

4. Z Score

3. Standard Deviation

2. Normal Distribution Illustration

1. Normal Distribution


Normal Distribution

Known by a variety of names - normal curve, bell curve, normal distribution, or Gaussian distribution (Wagner & Gillespie, 2018)It is a fundamental concept in statistics showing distribution that is often used to model real-world dataKey characteristics: - bell curve - mean and median - constant standard deviatin

Note. From Pritha Bhandari [image}, by Scribbler, 2023https://www.scribbr.com/statistics/normal-distribution/
Figure 1A normal distribution illustration

Normal Distribution Illustration

  • Mean is the center line of the bell curve
  • Each line before and after the mean represents one standard deviation
  • The entire range of data should be present in the curve

This is known as the 68-95-99.7 rule(McGregor, 2018)

  • 68% of raw scores fall within 1 SD
  • 95% of raw scores fall within 2 SD
  • 99.7% of raw scores fall within 3 SD
Note. From Pritha Bhandari [image}, by Scribbler, 2023https://www.scribbr.com/statistics/normal-distribution/
Figure 2A standard distribution illustration

Standard Deviation (SD)

SD represents the distance the data is from the mean (McGregor, 2018)

Z Score

Z score represents how many standard deviations (SD) a raw score is from the mean They can be helpful in an education setting. A student's score can be compared to the class average as opposed to looking at scores in isolation.

Normal Distribution Height

Mean determines the height of the curve Because mean is the most common possibility for a data point, it must be the heighest point of the curve

Lens to Consider

Probability vs. Standard Deviation

"In light of the data, what is the probability that the obtained results are due to chance?" (Nestor & Schutt, 2015, p. 11)

In a normal curve, there is a 68% chance of an occurrence happening within one standard deviation (McGregor, 2018)

Standard Deviation

Refers to the likelihood or chance of a particular event or outcome occurring. It is a measure of uncertainty or randomness associated with a given situation or experiment


Note. From Pritha Bhandari [image}, by Scribbler, 2023https://www.scribbr.com/statistics/normal-distribution/
Figure 3An empirical rule illustration


"A value that is significantly outside the interval of the rest of the scores in the distribution" (Wagner & Gillespie, 2018, p. 2017)

  • Normal distribution, often referred to as the bell curve, is a widely used statistical model with a bell-shaped curve
  • Standard deviation measures the extent of data dispersed around the mean in a set of data
  • Data points that significantly deviate from the rest of the data, potentially indicating errors or unusual phenomena


Bhandari, P. (2023, June 21). Standard normal distribution [Image]. Scribbler. https://www.scribbr.com/statistics/normal- distribution/McGregor, S. L. (2018). Understanding and evaluating research: A critical guide. SAGE Publications.Nestor, P. G., & Schutt, .R. K. (2015). Research methods in psychology (2nd ed.). Thousand Oaks, CA: Sage.Wagner, W. E., & Gillespie, B. J. (2018). Using and interpreting statistics in the social, behavioral, and health sciences. SAGE Publications.