Question

the lists show the heights, in inches, of the players on two basketball teams, the cranes the comets. heights of cranes players (inches) 73 75 76 77 77 78 78 80 82 82 83 75 78 80 heights of comets players (inches) 68 75 76 77 78 79 79 81 81 82 83 75 76 79 80 complete the sentences. the median height for the cranes is the median height for the comets. if the outlier were removed, the median height for the cranes would , and the median height for the comets would

Explanation:

Step1: Arrange Cranes' heights in ascending order

$73,75,75,76,77,77,78,78,78,80,80,82,82,83$
There are $n = 14$ data - points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=7$ and $\frac{n}{2}+1 = 8$. The 7th value is $78$ and the 8th value is $78$. So the median of Cranes' heights is $\frac{78 + 78}{2}=78$.

Step2: Arrange Comets' heights in ascending order

$68,75,75,76,76,77,78,79,79,79,80,81,81,82,83$
There are $n = 15$ data - points. The median is the $(\frac{n + 1}{2})$th ordered value. $\frac{n+1}{2}=\frac{15 + 1}{2}=8$. The 8th value is $79$.

Step3: Compare the medians

Since $78<79$, the median height for the Cranes is less than the median height for the Comets.

Step4: Identify the outlier and recalculate medians

The outlier in the Cranes' data is $73$ (it is far from the other values). After removing $73$, there are $n = 13$ data - points. The median is the $(\frac{n + 1}{2})$th ordered value. $\frac{n+1}{2}=\frac{13+1}{2}=7$. The 7th value in the new ordered list ($75,75,76,77,77,78,78,78,80,80,82,82,83$) is $78$, so the median remains the same.
For the Comets, there is no obvious outlier. Removing an outlier (if we assume there is none) or not, the median of the Comets' data remains $79$ as it is not affected by non - existent outliers.

Answer:

The median height for the Cranes is less than the median height for the Comets.
If the outlier were removed, the median height for the Cranes would stay the same, and the median height for the Comets would stay the same.