Question

mr. lowe is a school librarian. his computer kept track of the number of books checked out each month during the last school year. which box plot represents the data?

Explanation:

Step1: Order the data

First, we order the data set: \(2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500\)

Step2: Find the minimum, maximum, median, Q1, Q3

- Minimum (\( \text{min} \)): \(2500\)
- Maximum (\( \text{max} \)): \(7500\)
- Median (middle value of ordered data, since \(n = 10\), average of 5th and 6th values): \(\frac{4247 + 4753}{2} = \frac{9000}{2} = 4500\)
- Q1 (median of lower half: \(2500, 2712, 3500, 3876, 4247\)): 3500
- Q3 (median of upper half: \(4753, 4983, 5000, 6214, 7500\)): 5000

Step3: Analyze the box - plots

A box - plot has a box from Q1 to Q3, a line inside the box at the median, and whiskers from the minimum to Q1 and from Q3 to the maximum.
- For the first box - plot: The median line should be at 4500, Q1 at 3500, Q3 at 5000, min at 2500, max at 7500.
- For the second box - plot: The positions of Q1, median, Q3 should match our calculations. The median is 4500, Q1 is 3500, Q3 is 5000. Looking at the two box - plots, the second box - plot (the one with the box where the median line and quartile positions match our calculated values) is the correct one. Wait, actually, let's re - check. Wait, the first box - plot: Let's see the box. Wait, no, let's re - order the data correctly. Wait, the data points are: 2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500. So lower half (first 5 numbers): 2500, 2712, 3500, 3876, 4247. The median of lower half (Q1) is the 3rd number, which is 3500. Upper half (last 5 numbers): 4753, 4983, 5000, 6214, 7500. The median of upper half (Q3) is the 3rd number, which is 5000. Median of all data: (4247 + 4753)/2 = 4500. Now, looking at the two box - plots: The first box - plot has the box with Q1 around 3500, median around 4500, Q3 around 5000? Wait, no, the second box - plot: Wait, maybe I made a mistake. Wait, the first box - plot: Let's check the whiskers. Wait, the minimum is 2500, maximum is 7500. The box is from Q1 to Q3. Q1 = 3500, Q3 = 5000, median = 4500. Now, looking at the two box - plots, the second box - plot (the one where the median line is at 4500, Q1 at 3500, Q3 at 5000) is the correct one? Wait, no, wait the first box - plot: Wait, the first box - plot's box: Let's see the numbers on the axis: 2500, 3500, 4500, 5500, 6500, 7500. The first box - plot: The left whisker is from 2500 to Q1 (3500), the box is from Q1 (3500) to Q3 (5000), with median at 4500, and the right whisker from Q3 (5000) to max (7500). Wait, no, the first box - plot: Wait, the user's first box - plot: Let me re - examine. Wait, the first box - plot: The box is split, with the left part of the box up to around 3500 - 4500? No, wait, the correct box - plot should have Q1 = 3500, median = 4500, Q3 = 5000. So the box is from 3500 (Q1) to 5000 (Q3), with a line at 4500 (median). The whiskers are from 2500 (min) to 3500 (Q1) and from 5000 (Q3) to 7500 (max). So the second box - plot (the one where the box is from Q1 = 3500 to Q3 = 5000, median at 4500) is the correct one. Wait, no, maybe I mixed up the two. Wait, the first box - plot: Let's see the numbers on the x - axis: 2500, 3500, 4500, 5500, 6500, 7500. The first box - plot: The left whisker is from 2500 to 3500, the box is from 3500 to 5000? No, the first box - plot's box is two parts, with the left part up to around 3500 - 4500? Wait, no, the correct box - plot should have Q1 = 3500, median = 4500, Q3 = 5000. So the box is from 3500 to 5000, median at 4500. The second box - plot (the one below the first one in the image) has the box where the median line is at 4500, Q1 at 3500, Q3 at 5000. So the second box - plot (the one with the box that has the median line and quartile positions matching our calculated Q1 = 3500, median = 4500, Q3 = 5000) is the correct representation of the data.

Answer:

The second box - plot (the one with the title "Books checked out" and the box where the median, Q1, and Q3 positions match the calculated values of median = 4500, Q1 = 3500, Q3 = 5000, min = 2500, max = 7500)