Suppose every student in your class got a score of 85% on an exam. What are the mean and standard deviation of those exam scores without doing any calculations?
I want to say the mean is 100 and the standard deviation is 1 but I don't know why. If all students scored 85% that would be 100% of them so that's how I got 100 but I don't understand how to reach the standard deviation.
Ummmh, if everybody got an 85, wouldn't the average be 85 ??? , so mean = 85
and since nobody "deviated" from that score, wouldn't the standard deviation be zero ????
Suppose the scores of students on an exam are normally distributed with a mean of 507 and a standard deviation of 97. According to the empirical rule, what percentage of students scored between 410 and 604 on the exam?
To calculate the mean and standard deviation of the exam scores without doing any calculations, we can use the properties of a normal distribution.
The mean is the average value of a set of numbers. In this case, since all students scored 85%, the mean will also be 85%. The mean is not 100 because the scores are not distributed evenly around 100.
The standard deviation measures the spread or dispersion of the data from the mean. In this case, since all students scored the same percentage, there is no variation or spread in the data. As a result, we can say that the standard deviation is 0, rather than 1.
To determine the mean and standard deviation of the exam scores without performing any calculations, you can make a few observations:
1. Mean: In this case, all students in your class scored 85% on the exam. Therefore, since every student has the same score, the mean score will also be 85%. It does not necessarily mean the mean will be 100; it will be equal to the score obtained by all students, i.e., 85%.
2. Standard Deviation: The standard deviation measures the spread or variability of the data. In this scenario, all students have the exact same score, 85%. As a result, there is no variability or spread in the data, indicating that the standard deviation will be zero. This is because every score is identical to the mean, resulting in no variation from the mean.
So, the mean of the exam scores is 85% and the standard deviation is zero.