Suppose a large number of people take a take and every single student gets half of the answers correct. In this case, the standard deviation is:
A) Equal to the mean
B) Equal to the median
C) Equal to zero
D) Impossible to determine without more information
If all are the same, the standard deviation is zero.
In this case, the standard deviation cannot be determined without more information. The information provided only states that every single student gets half of the answers correct, but it does not mention the specific scores or the distribution of the scores. Therefore, without additional information, it is impossible to determine the standard deviation. The correct answer is D) Impossible to determine without more information.
To find the standard deviation in this scenario, we need to calculate the variance first. The variance is the average of the squared deviations from the mean.
In this case, since every student gets half of the answers correct, we know that for each student, the deviation from the mean is always going to be 0. This is because half of the answers correct is the mean in this case.
Therefore, the variance is also going to be 0, because the squared deviation from the mean is always going to be 0.
To find the standard deviation, we take the square root of the variance. Since the variance is 0, the square root of 0 is also 0.
Therefore, the standard deviation in this case is equal to zero.
So, the correct answer is option C) Equal to zero.