Question

83

EDFN 1090/1092
Assignment 4
1. From statistics grades, John has a mean of 70 and Sx(standard deviation) of 15, Jane
has a mean of 70 and Sx(standard deviation) of 5. Hint: create a 68% Range)
Describe the two students in terms of consistency of their grades and give reason.

Answer 1

Jane's grades are more consistent than John's, as indicated by her smaller standard deviation of 5, compared to John's standard deviation of 15. This consistency is reflected in the narrower range of scores around the mean for Jane.

Step-by-step explanation:

When comparing John and Jane in terms of the consistency of their grades, we must consider their respective means and standard deviations. Both have the same mean score of 70, but their standard deviations differ. John's standard deviation is 15, while Jane's standard deviation is 5. The standard deviation indicates how spread out the grades are. A smaller standard deviation means that the grades are more consistently close to the mean.

Creating a 68% Range (referring to the empirical rule or 68-95-99.7 rule) for each student, we can find the range of grades that contain about 68% of their scores. For John, the range is 70 ± 15 (which is 55 to 85), and for Jane, it is 70 ± 5 (which is 65 to 75). Therefore, Jane's grades are more consistent, as her scores fall within a tighter range around the mean, as opposed to John's scores which are more spread out.

Answer 2

68% of the time, John's grades will be between 55 and 85, while for Jane, 68% of the time, her grades will be between 65 and 75. They have the same mean grade, however, due to the lower standard deviation, Jane is more consistent, while John has the higher upside.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

John:

Mean of 70, standard deviation of 15.

70 - 15 = 55

70 + 15 = 85

68% of the time, John's grades will be between 55 and 85.

Jane:

Mean of 70, standard deviation of 5.

70 - 5 = 65

70 + 6 = 75.

68% of the time, Jane's grades will be between 65 and 75.

Describe the two students in terms of consistency of their grades and give reason.

68% of the time, John's grades will be between 55 and 85, while for Jane, 68% of the time, her grades will be between 65 and 75. They have the same mean grade, however, due to the lower standard deviation, Jane is more consistent, while John has the higher upside.