Question

question #1 the list below shows the most recent test scores for students in mr. garcias study group. 78, 90, 94, 72, 80, 68, 72, 88, 94, 98, 86, 96 which box - and - whisker plot correctly represents the data in the list?

Explanation:

Step1: Arrange data in ascending order

$68,72,72,78,80,86,88,90,94,94,96,98$

Step2: Find the minimum and maximum values

Minimum = $68$, Maximum = $98$

Step3: Find the median (Q2)

Since there are 12 data - points, the median is the average of the 6th and 7th values. $\text{Median}(Q2)=\frac{86 + 88}{2}=87$

Step4: Find the lower half and upper half of data

Lower half: $68,72,72,78,80,86$. Upper half: $88,90,94,94,96,98$

Step5: Find Q1 and Q3

Q1 is the median of the lower half. Since there are 6 values in the lower half, $Q1=\frac{72+78}{2}=75$. Q3 is the median of the upper half. Since there are 6 values in the upper half, $Q3=\frac{94 + 94}{2}=94$

The box - and - whisker plot should have the minimum value at 68, Q1 at 75, median at 87, Q3 at 94, and maximum at 98.

Answer:

Based on the above - calculated values, we need to visually inspect the plots to find the one that matches these values. Without seeing the exact details of the box - and - whisker plots in a more precise way (since we can't directly interact with the image), but if we assume the correct positioning of the box (from Q1 to Q3) and the median line within the box and the whiskers from the minimum to Q1 and Q3 to the maximum, we can conclude that the correct box - and - whisker plot is the one that has the box starting at 75, ending at 94, with a line inside the box at 87, and whiskers extending to 68 and 98. If we had to make a choice among the options presented in a multiple - choice format, we would choose the plot that adheres to these values. Since no specific visual inspection is possible here in a digital text - based response, the key is to know that the box should span from 75 to 94, the median line should be at 87, and the whiskers should go to 68 and 98.