For a particular sample of 63 scores on a psychology exam, the following results were obtained.

First quartile = 57 Third quartile = 87 Standard deviation = 9 Range = 51
Mean = 72 Median = 72 Mode = 98 Midrange = 57

I. What score was earned by more students than any other score? Why?
II. What was the highest score earned on the exam?
III. What was the lowest score earned on the exam?
IV. According to Chebyshev's Theorem, how many students scored between 45 and 99?
V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 45 and 99?

Confused! How do i do this??

I can help you find the answers to these questions. Let's go through each question step by step:

I. What score was earned by more students than any other score? Why?
To find the score that was earned by more students than any other score, we need to look at the mode. The mode represents the value(s) that appear most frequently in the data set. In this case, the mode is given as 98. Therefore, 98 was earned by more students than any other score.

II. What was the highest score earned on the exam?
To find the highest score earned on the exam, we need to look at the range. The range is the difference between the highest and lowest values in the data set. Here, the range is given as 51. Since the lowest score is not provided, we can calculate the highest score by adding the range to the lowest score.

The formula to find the highest score is:
Highest Score = Lowest Score + Range

III. What was the lowest score earned on the exam?
As mentioned earlier, the lowest score is not directly provided. However, we can calculate it by subtracting the range from the highest score.

The formula to find the lowest score is:
Lowest Score = Highest Score - Range

IV. According to Chebyshev's Theorem, how many students scored between 45 and 99?
Chebyshev's Theorem states that, for any given number of standard deviations, k, at least (1 - 1/k^2) of the data falls within that range. In this case, the standard deviation is given as 9.

Since the range from 45 to 99 covers 54 units, the number of standard deviations away from the mean for the lower bound (45) is:
(45 - Mean) / Standard Deviation

Similarly, for the upper bound (99):
(99 - Mean) / Standard Deviation

By applying Chebyshev's Theorem with a given number of standard deviations and using the formula, we can estimate the proportion of data falling within the range. However, it does not provide an exact number of students, only a minimum proportion.

V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 45 and 99?
The Empirical Rule (also known as the 68-95-99.7 rule) is applicable when the distribution is normal. It states that:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.

Using this rule, we can estimate the proportion of data falling within the range of 45 to 99. However, we still cannot determine the exact number of students, only the proportion based on the empirical rule.

Please provide the mean value of the exam scores so that I can calculate the remaining values and answer your questions accurately.