Question

i want to select average students. If the mean score on the qualifying test is 43.2, and the standard deviation is 8.6 find the scores that cut off the middle 50% of ALL scores

Answer 1

We assume here that we have a normal distribution. In this kind of distribution, the mean is the center of this distribution. We also have that the mean, the median, and the mode are the same in a Normal Distribution and all of them cut off the middle 50%.

Therefore, the score that cut off the middle %50 is the mean (43.2). The distribution can be represented graphically as follows (this is a normal distribution with a mean = 43.2, and a standard deviation of 8.6):

If we can see carefully, we have:

The value that cut off the middle 50% of all the scores is the mean = 43.2 ---50% of the values are below the mean (and also the median, and the mode), and the other 50% are above this value (43.2).