Question

draw a box - and - whisker plot for the set of data. 23.5, 18.2, 3.3, 23.3, 11.3, 18.8, 78.8, 69.1, 2.2, 16.1, 54.9, 44.8, 37.4 a. a box - and - whisker plot diagram b. a box - and - whisker plot diagram c. a box - and - whisker plot diagram d. a box - and - whisker plot diagram please select the best answer from the choices provided

Explanation:

Step1: Arrange data in ascending order

$2.2,3.3,11.3,16.1,18.2,18.8,23.3,23.5,37.4,44.8,54.9,69.1,78.8$

Step2: Find the median (Q2)

There are 13 data - points. The median is the 7th value. So, $Q2 = 23.3$.

Step3: Find the lower half of data

$2.2,3.3,11.3,16.1,18.2,18.8$
The median of the lower half (Q1) is the average of the 3rd and 4th values. $Q1=\frac{11.3 + 16.1}{2}=13.7$.

Step4: Find the upper half of data

$23.5,37.4,44.8,54.9,69.1,78.8$
The median of the upper half (Q3) is the average of the 3rd and 4th values. $Q3=\frac{44.8+54.9}{2}=49.85$.

Step5: Identify the minimum and maximum

The minimum value is $2.2$ and the maximum value is $78.8$.

Step6: Analyze box - and - whisker plot features

The box starts at Q1 ($13.7$), ends at Q3 ($49.85$), has a line at Q2 ($23.3$), the left - whisker extends to the minimum ($2.2$) and the right - whisker extends to the maximum ($78.8$).

Answer:

By comparing the calculated values of minimum, Q1, Q2, Q3, and maximum with the given box - and - whisker plots, we can determine the correct plot. Without seeing the visual details of the plots in a more clear way, we assume that the plot with the minimum around 2.2, Q1 around 13.7, Q2 around 23.3, Q3 around 49.85 and maximum around 78.8 is the correct one. But if we had to choose based on the steps above, we need to visually inspect the plots to pick the one that matches these values. If we assume the plots are drawn accurately, we would pick the plot that has these correct endpoints for the box and whiskers. Since no specific visual inspection is possible here other than the values, we can't definitively say which lettered option (A, B, C, D) it is without more visual clarity on the plots. But the correct plot should have a box starting near 13.7, ending near 49.85, a line in the box near 23.3, a left - whisker starting at 2.2 and a right - whisker ending at 78.8.