The midterm and final exam grades for a statistics course are provided in the data set below. Jaymes, a student in the class, scored 86 on both exams. Treat the given data sets as samples. Midterm: 80, 78, 85, 82, 79, 79, 78, 86, 80, 84, 78, 84, 80, 84, 81, 78, 81, 82, 78, 84 Final: 81, 88, 68, 69, 69 81, 82, 86, 76, 71, 72, 68, 77, 86, 68, 83, 84, 71, 81, 87 z-score for midterm: 1.857 z-score for final: 1.181 Based on the z-scores calculated above, which of Jaymes's grades is more unusual, the midterm grade or the final exam grade? Select the correct answer below: A. The absolute value of the z-score for the final exam grade is greater than for the midterm grade, so the final exam grade is more unusual. B. The absolute value of the z-score for the midterm exam grade is less than for the final grade, so the midterm grade is more unusual. C. The absolute value of the z-score for the midterm exam grade is greater than for the final grade, so the midterm grade is more unusual. D. The absolute value of the z-score for the final exam grade is less than for the midterm grade, so the final exam grade is more unusual.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The midterm and final exam grades for a statistics course are provided in the data set below. Jaymes, a student in the class, scored 86 on both exams. Treat the given data sets as samples.
Midterm: 80, 78, 85, 82, 79, 79, 78, 86, 80, 84, 78, 84, 80, 84, 81, 78, 81, 82, 78, 84
Final: 81, 88, 68, 69, 69 81, 82, 86, 76, 71, 72, 68, 77, 86, 68, 83, 84, 71, 81, 87
z-score for midterm: 1.857
z-score for final: 1.181
Based on the z-scores calculated above, which of Jaymes's grades is more unusual, the midterm grade or the final exam grade?
- Select the correct answer below:
A. The absolute value of the z-score for the final exam grade is greater than for the midterm grade, so the final exam grade is more unusual.
B. The absolute value of the z-score for the midterm exam grade is less than for the final grade, so the midterm grade is more unusual.
C. The absolute value of the z-score for the midterm exam grade is greater than for the final grade, so the midterm grade is more unusual.
D. The absolute value of the z-score for the final exam grade is less than for the midterm grade, so the final exam grade is more unusual.
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