If the mean of this distribution is 13.7, which could NOT be the median?
A) 9
B) 14
C) 16 ***
D) 18
depends on the data. I could easily come up with a data set giving any of the choices for the mean.
I need the answer
To determine which value could not be the median given that the mean is 13.7, we need to understand the relationship between the mean and median.
The mean is the average of all the data points in a distribution, while the median is the middle value. In other words, if we arrange the data points in ascending or descending order, the median is the value in the middle.
In a symmetric distribution, the mean and median are the same. However, in a skewed distribution, the mean and median may be different. Specifically, in a positively skewed distribution (long tail on the right), the mean will be greater than the median.
In this case, the mean is given as 13.7. This means that if we were to arrange the data in order, the average value would be close to 13.7.
Now let's consider the options:
A) 9: This could be the median. If we arrange the data in ascending order and assign 9 as the median, it is possible to have data values both above and below 9 that would average out to approximately 13.7. So option A is a valid choice.
B) 14: This could be the median. If we arrange the data in ascending order and assign 14 as the median, it is possible to have data values both above and below 14 that would average out to approximately 13.7. So option B is a valid choice.
C) 16: This could not be the median. Since the mean is given as 13.7, if we arrange the data in ascending order and assign 16 as the median, there would need to be values below 16 that would bring the average down to 13.7. This is not possible because 16 is already greater than the mean. Therefore, option C cannot be the median.
D) 18: This could be the median. If we arrange the data in ascending order and assign 18 as the median, it is possible to have data values both above and below 18 that would average out to approximately 13.7. So option D is a valid choice.
So, the value that could NOT be the median is C) 16.