Question

this list shows the heights in feet of the 30 tallest mountains in the united states. 14,269 14,361 14,470 14,831 16,237 14,270 14,370 14,494 14,950 16,390 14,286 14,410 14,500 15,300 16,500 14,294 14,420 14,530 15,638 17,400 14,309 14,421 14,573 15,885 18,008 14,345 14,433 14,730 15,979 20,320 what is the median of the mountain data? a. 14,500 ft b. 14,515 ft c. 14,530 ft d. 14,573 ft please select the best answer from the choices provided

Explanation:

Step1: Arrange data in ascending order

The data is already in a list - no need to re - arrange as it's not specified to be out of order. Since there are $n = 30$ data points (an even number of data points).

Step2: Use median formula for even - numbered data set

The median formula for an even - numbered data set is $\text{Median}=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $\frac{n}{2}=\frac{30}{2}=15$ and $\frac{n}{2}+1 = 16$.

Step3: Identify the 15th and 16th ordered data values

Counting through the list, the 15th value is $14500$ and the 16th value is $14530$.

Step4: Calculate the median

$\text{Median}=\frac{14500 + 14530}{2}=\frac{29030}{2}=14515$

Answer:

b. 14,515 ft