The Following Data Represent the Scores of a Sample of 50

question 174

Essay

The following data represent the scores of a sample of 50 students on a statistics exam. The mean score is $\bar { x } = 80.3 \text {, and the standard deviation is } s = 11.37$

$\begin{array} { l l l l l l l l l l } 49 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\ 71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\ 79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\ 85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\ 90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 98 \end{array}$
What percentage of the scores fall in each of the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$ , and $\bar { x } \pm 3 s$ ? Based on these percentages, do you believe that the distribution of scores is approximately normal? Explain.

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Definitions:

Pessimistic Attributional

A tendency to blame negative outcomes on stable, internal factors within oneself, expecting future failures.

Learned Helplessness

Through experience with unavoidable aversive stimuli, an organism learns that it has no control over negative outcomes.

Psychological Factors

Elements of a person's psychological state that influence their behavior and well-being, such as attitudes, emotions, and motivations.

Depressive Disorder

A mood disorder characterized by persistent feelings of sadness, hopelessness, and loss of interest in activities, often accompanied by physical symptoms.