Question

a snowstorm hit dane county. a weatherman reported how many inches of snow each city in the area received. snowfall (in.) 4 3 6 5 4 5 7 6 5 3 which box plot represents the data? snowfall (in.) snowfall (in.)

Explanation:

Step1: Arrange data in ascending order

3, 3, 4, 4, 5, 5, 5, 6, 6, 7

Step2: Find the minimum value

The minimum value is 3.

Step3: Find the first - quartile ($Q_1$)

There are $n = 10$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{10+ 1}{4}=2.75$. So, $Q_1=3+(4 - 3)\times0.75 = 3.75$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 10$ (even number of data points) is $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. So, $Q_2=\frac{5 + 5}{2}=5$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So, $Q_3=6+(6 - 6)\times0.25 = 6$.

Step6: Find the maximum value

The maximum value is 7.

Answer:

The box - plot should have the minimum value at 3, $Q_1$ at approximately 3.75, the median at 5, $Q_3$ at 6, and the maximum value at 7. Without seeing the full set of box - plot options clearly, based on these values, you can identify the correct box - plot. The box will start at $Q_1\approx3.75$, end at $Q_3 = 6$, have a line inside the box at the median 5, and the whiskers will extend to the minimum 3 and maximum 7.