RES6003 Mod 2 Assign - Techau

RES6003

Features of Normal Distribution

Monica Techau Dr. Don Demoulin

INDEX

1. Normal Distribution

2. Normal Distribution Illustration

3. Standard Deviation

4. Z Score

5. Normal Distribution Height

6. Probability vs. Standard Deviation

7. Outliers

8. Summary

9. References

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 data Key characteristics: - bell curve - mean and median - constant standard deviatin

Figure 1A normal distribution illustration

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

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

Figure 2A standard distribution illustration

Standard Deviation (SD)

SD represents the distance the data is from the mean (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

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

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

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

Probability vs. Standard Deviation

Lens to Consider

Standard Deviation

Probability

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

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

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

Outliers

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)

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

Summary

• 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

References

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.