when hector opened his cupcake shop, he wanted to make sure his cupcakes were as fresh as possible. in the…
when hector opened his cupcake shop, he wanted to make sure his cupcakes were as fresh as possible. in the first few days, he counted how many cupcakes were leftover every day. leftover cupcakes 16 31 12 28 28 20 22 22 32 16 14 25 which box plot represents the data? leftover cupcakes leftover cupcakes
Answer
Explanation:
Step1: Arrange data in ascending order
$12, 14, 16, 16, 20, 22, 22, 25, 28, 28, 31, 32$
Step2: Find the minimum value
The minimum value is $12$.
Step3: Find the first - quartile ($Q_1$)
There are $n = 12$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{12+1}{4}=3.25$. So, $Q_1=16$.
Step4: Find the median ($Q_2$)
The position of the median for $n = 12$ is $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. So, $Q_2=\frac{22 + 22}{2}=22$.
Step5: Find the third - quartile ($Q_3$)
The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75$. So, $Q_3=28$.
Step6: Find the maximum value
The maximum value is $32$.
Step7: Analyze box - plots
The left - most whisker starts at the minimum value ($12$), the box starts at $Q_1 = 16$, the line inside the box is at the median $Q_2=22$, the box ends at $Q_3 = 28$, and the right - most whisker ends at the maximum value ($32$). The first box - plot represents these values correctly.