Question

part 1 of 6 (a) could the mean be one of the numbers in the data set?
yes
no
part: 1 / 6
part 2 of 6 (b) when would the median be one of the numbers in the data set?
the median is one of the numbers in the data set if the data set has an select number of items, or if the data set has an even number of items and the two middle items are select

Explanation:

Part 1 of 6 (a)

The mean is the average of a data set. For example, in the data set {2, 2, 2}, the mean is $\frac{2 + 2 + 2}{3}=2$, which is in the data set. So the mean can be one of the numbers in the data set.

1. Recall the definition of the median: when the data set is ordered, if there are an odd number of items, the median is the middle - most number (which is in the data set). If there are an even number of items, the median is the average of the two middle - most numbers. So the median is one of the numbers in the data set if the data set has an odd number of items, or if the data set has an even number of items and the two middle items are equal (because then their average is equal to themselves, so the median is in the data set).
2. For the first blank: The median is the middle value when the data is ordered. If the number of items $n$ is odd, say $n = 2k+1$ for some integer $k$, then the median is the $(k + 1)$ - th value, which is one of the data points. If $n$ is even, $n=2k$, the median is $\frac{x_{k}+x_{k + 1}}{2}$. For this to be equal to a data point, $x_{k}=x_{k + 1}$.

Answer:

Yes

Part 2 of 6 (b)