ellen works as a train conductor. on her last route, she counted the number of riders who got on at each…
ellen works as a train conductor. on her last route, she counted the number of riders who got on at each stop.\nnew riders\n11 16 3 2 0 8 2 6 0 9 14 4 8\nwhich box plot represents the data?\nnew riders\nnew riders
Answer
Explanation:
Step1: Arrange data in ascending order
$0,0,2,2,3,4,6,8,8,9,11,14,16$
Step2: Find the minimum value
The minimum value is $0$.
Step3: Find the first - quartile ($Q_1$)
There are $n = 13$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{13+1}{4}=3.5$. So, $Q_1=\frac{2 + 2}{2}=2$.
Step4: Find the median ($Q_2$)
The position of the median is $\frac{n + 1}{2}=\frac{13+1}{2}=7$. So, $Q_2 = 6$.
Step5: Find the third - quartile ($Q_3$)
The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(13 + 1)}{4}=10.5$. So, $Q_3=\frac{9+11}{2}=10$.
Step6: Find the maximum value
The maximum value is $16$.
Step7: Analyze box - plots
The box - plot should have the minimum at $0$, $Q_1$ at $2$, median at $6$, $Q_3$ at $10$ and maximum at $16$. The first box - plot has these characteristics.