Question

to create a box plot, you need to find the minimum, first quartile, median, third quartile, and maximum values for the data set. these 5 values are sometimes called the five - number summary. drawing a vertical mark and then connecting the pieces as in the example creates the box plot. for the ph box plot, we can see that the minimum is about 5.8, the median is about 7.4, and the third quartile is around 7.9.

Explanation:

Since the problem seems to be about analyzing a box - plot related to pH data and maybe finding some missing values in the five - number summary (like first quartile or maximum), let's assume we need to find the first quartile or maximum. But the problem statement is a bit incomplete. However, if we assume we need to find the first quartile (Q1) using the median (Q2 = 7.4) and third quartile (Q3 = 7.9) and the fact that in a box - plot, the box is between Q1 and Q3, and the median is inside the box.

Step - by - Step Explanation (assuming we want to find Q1, and we know that the distance between Q1 and Q2 and Q2 and Q3 can be related, but maybe from the number line, the box starts around 6.8? Wait, the number line has marks at 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9. The box is between two rectangles. Let's re - evaluate.

Wait, the text says minimum is ~5.8, median ~7.4, Q3 ~7.9. Let's assume we need to find Q1. In a box - plot, the box spans from Q1 to Q3, and the median is inside. The length of the box (IQR = Q3 - Q1). If we look at the number line, the box is between, say, 6.8 and 7.9? Wait, no, the median is 7.4, which is inside the box. Let's calculate Q1.

If we assume the data is symmetric (not necessarily, but for illustration), but maybe from the number line, the left end of the box (Q1) is around 6.8? Wait, the minimum is 5.8, median 7.4, Q3 7.9. Let's calculate IQR = Q3 - Q1. But we can also think that the distance from Q1 to median and median to Q3. If median is 7.4 and Q3 is 7.9, the distance is 0.5. So Q1 would be 7.4 - 0.5 = 6.9? But maybe from the number line, the first quartile is around 6.8.

But since the problem is not well - defined, if we assume we need to find the first quartile:

Step 1: Recall the five - number summary components

The five - number summary is minimum (min), first quartile (Q1), median (Q2), third quartile (Q3), maximum (max). We know min≈5.8, Q2≈7.4, Q3≈7.9.

Step 2: Estimate Q1 from the box - plot

Looking at the box - plot, the left side of the box (Q1) is around 6.8 (by visually inspecting the number line where the box starts). Alternatively, if we use the fact that in a box - plot, the box is between Q1 and Q3, and the median is in the middle. The distance between Q3 (7.9) and median (7.4) is 7.9 - 7.4 = 0.5. So the distance between median (7.4) and Q1 should be approximately the same if the data is symmetric, so Q1≈7.4 - 0.5 = 6.9.

Since the problem is not fully specified, if we assume the question is to find Q1, a possible answer is approximately 6.8 - 6.9.

If the question was to find the maximum, looking at the number line, the maximum is around 8.8 (since the whisker on the right ends near 8.8).

But since the original problem is a bit unclear, if we take the information given and assume we need to find Q1:

Answer:

Approximately 6.8 (or 6.9, depending on the method of estimation)