Discussion Reply
1. Something I found interesting about the normal distribution is the z-score; it is an interesting concept in normal distribution because it allows us to standardize data and compare values from different distributions on a common scale. The z-score can also be used to compare data from different normal distributions. By converting data to z-scores, we can compare observations from different distributions on a common scale and determine which observation is relatively larger or smaller (Gravetter & Wallnau, 2014). The z-score is really interesting because of all the information you can obtain from it.
One interesting property of the z-score is that it can be used to calculate percentiles for a normal distribution. For example, a z-score of 1.645 corresponds to the 95th percentile of a standard normal distribution, which means that 95% of the data falls below this value (Field et al., 2012).
Another interesting thing about the normal distribution is the rule known as the 68-95-99.7 rule, which states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations (Navidi, 2015). This is really interesting to me because of how much information you can gain from it. As well as how it is true so often, it seems like the rule would be rare but the fact that it is normal for data to be that exact way is really interesting.
Resources:
Field, A., Miles, J., & Field, Z. (2012). Discovering statistics using R. Sage.
Gravetter, F. J., & Wallnau, L. B. (2014). Statistics for the behavioral sciences (9th ed.). Cengage Learning.
Navidi, W. (2015). Statistics for engineers and scientists (4th ed.). McGraw Hill.
2. Unlike last week’s chapter, there appears to be less of a danger when considering normal distribution in statistics. All normal distributions have the same bell shape, knowing the mean and standard deviation of a distribution allows us to know much about where the data values lie (Bennett, 2018). Using a bell-shaped curve representing the mean at the top of the curve provides a clearer understanding of the statistics represented. Having a clearer understanding of statistics allows data to be less likely to be skewed because the normal distribution is zero unlike a distribution of left or right skewed that was explained in Chapter Four of the textbook.
Reference
Bennett, J. O., Briggs, W. L., & Triola, M. F. (2018). Statistical reasoning for everyday life. Pearson.
Create a reply for each discussion post presented. In response to your peers, comment on facts about the normal distribution your peers have posted, supporting your response by explaining why it captures your interest or describing how the principle can be applied in psychology and/or everyday life.
