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?

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?

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 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 12 data points is $\frac{n+1}{2}=\frac{12 + 1}{2}=6.5$. 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.

Answer:

The box - plot with minimum value 12, $Q_1 = 16$, $Q_2=22$, $Q_3 = 28$ and maximum value 32 is the correct one. (You would need to visually identify the correct box - plot from the given options based on these values).