Let's go one by one.
A: The distribution is, in fact, symmetric. I know this because if I were to draw a straight line, or hold up a mirror to the screen, both sides would match.
B: B is not true because there is only student who is the maximum age of 16, as compared to the majority of students who are 14.
C: Let's write down the data:
12, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 16
If we add all these up, we get 168. We then should divide by 12, the amount of data samples, which gives us 14.
The mean is 14.
Automatically, I see that the center is filled with 14. Even though there are 12 total data pieces, we will not need to find the middle of two of the numbers-because 14 and 14 are the same number.
The median is 14.
Because the mean and median are both 14, we can conclude that C is true.
D: Because the mode (or most common number) would also be 14, we can conclude instantly that the 14 we got from the mean and median is the best representation of students in the play. D is also true. As far as the best measure of center goes, I usually prefer the mean, but it is almost entirely situational.
1. Mean (The average is<u> almost</u> always reliable)
Non-example: (4,4,4,4,4,4,4,4,4,4,307) It is clear there is an outlier here, which could affect the data more than it needs to-therefore this is a non-example.
Please let me know if this was helpful, or if you have any questions! If you are able, I'd be grateful to receive a rating!
