The Following Data Represent the Scores of 50 Students on a Statistics

question 104

Essay

The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. $$\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array}$$ What percentage of the scores lies within one standard deviation of the mean? two standard deviations of the mean? three standard deviations of the mean? Based on these percentages, do you believe that the distribution of scores is mound-shaped and symmetric? Explain.

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Definitions:

Token Economy

A behavior modification system that utilizes tokens as reinforcement for desirable behaviors, which can be exchanged for rewards.

Modeling

The process of imitation or simulation, often used in learning or in the analysis of complex systems by replicating behaviors, patterns, or activities.

Self-Defeating Thoughts

Negative and often irrational beliefs or inner narratives that undermine one’s confidence and potential for success.

Cognitive-Behavioral

A therapeutic approach that addresses dysfunctional emotions, maladaptive behaviors, and cognitive processes through a combination of cognitive and behavioral techniques.