mrs. jonas brought a jar filled with jellybeans to school. some of her students guessed how many jellybeans…

Answer:

To determine the correct box - plot, we need to find the five - number summary (minimum, first quartile $Q_1$, median, third quartile $Q_3$, maximum) of the data set: 150, 200, 246, 211, 283, 350, 254, 180, 400, 317, 225, 300, 280, 189.

Step1: Sort the data

150, 180, 189, 200, 211, 225, 246, 254, 280, 283, 300, 317, 350, 400

Step2: Find the minimum

The minimum value is 150.

Step3: Find the maximum

The maximum value is 400.

Step4: Find the median

Since there are $n = 14$ data points, the median is the average of the 7th and 8th ordered values. $\text{Median}=\frac{246 + 254}{2}=250$

Step5: Find $Q_1$

The lower half of the data is 150, 180, 189, 200, 211, 225, 246. Since there are 7 data points in the lower half, $Q_1$ is the 4th value, so $Q_1 = 200$

Step6: Find $Q_3$

The upper half of the data is 254, 280, 283, 300, 317, 350, 400. Since there are 7 data points in the upper half, $Q_3$ is the 4th value of the upper - half, so $Q_3=300$

We need to visually check which box - plot has a minimum of 150, $Q_1 = 200$, median of 250, $Q_3 = 300$ and maximum of 400. Without the actual box - plot options labeled as A, B, etc., we can't give a final selection among them, but the correct box - plot should have the left - most whisker at 150, the left side of the box at 200, the line inside the box at 250, the right side of the box at 300 and the right - most whisker at 400.