Wk 5 Discussion 1 - Normal Distribution [due Thurs]
Due Thursday
In statistics, it is critical to know what is meant by a normal distribution.
Write a 250- to 300-word response to the following:
What are the properties of a normal distribution?
normal distribution: A bell-shaped and symmetrical theoretical distribution with the mean, the median, and the mode all coinciding at its peak and with the frequencies gradually decreasing at both ends of the curve. ALSO LOOK FOR DEFINITION IN WEEK 1 DISCUSSION
The normal curve (Figure 5.1) is bell shaped. One of the most striking characteristics of the normal distribution is its perfect symmetry. If you fold Figure 5.1 exactly in the middle, you have
two equal halves, each the mirror image of the other. This means that precisely half the observations fall on each side of the middle of the distribution
In addition, the midpoint of the normal curve is the point having the maximum frequency. This is also the point at which three measures coincide: (1) the mode (the point of the highest frequency), (2) the median (the point that divides the distribution into two equal halves), and (3) the mean (the average of all the scores). Notice also that most of the observations are clustered
around the middle, with the frequencies gradually decreasing at both ends of the distribution.
Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2019). Social statistics for a diverse society
(9th ed.). SAGE Publications.
Is a normal distribution always necessary? Why or why not?
The normal curve is pivotal in much of statistics. Converting data to their normal curve equivalent values allows an incredibly diverse range of statistical techniques to be applied. This portion of statistics is involved with
z
scores, the normal curve equivalent values. These values are measured in
standard deviation units,
covered later in the book/ it accurately describes the distribution of values for many natural phenomena
.
Keller, D. K. (2006). Bell-shaped the normal curve. SAGE Publications, Inc., https://doi.org/10.4135/9781452226637
Why do researchers often refer to a normal distribution as a theoretical normal distribution
?
The normal distribution is a theoretical distribution, similar to an empirical distribution in that it
can be organized into frequency distributions, displayed using graphs, and described by its
