Question

ms. miller’s english class kept track of how many books they read last school year.
books read
41, 24, 97, 67, 103, 75, 120, 27, 53, 39, 108, 49, 111, 84, 44, 20
which box plot represents the data?
two box plots labeled books read with horizontal axes from 20 to 120, each with a box and whiskers

Explanation:

Step1: Order the data

First, we order the data set: \(20, 24, 27, 39, 41, 44, 49, 53, 67, 75, 84, 97, 103, 108, 111, 120\)

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

• Minimum: \(20\)
• To find Q1 (first quartile), we take the median of the lower half. The lower half is \(20, 24, 27, 39, 41, 44, 49, 53\). The median of this is \(\frac{41 + 44}{2} = 42.5\)? Wait, no, wait the number of data points: 16 data points. So the median is the average of the 8th and 9th terms. Wait, 16 data points: positions 1 - 16. Median is between 8th and 9th. 8th term is \(53\), 9th term is \(67\)? Wait no, wait ordered data: let's count again. Wait 16 numbers:

1:20, 2:24, 3:27, 4:39, 5:41, 6:44, 7:49, 8:53, 9:67, 10:75, 11:84, 12:97, 13:103, 14:108, 15:111, 16:120.

So median (Q2) is average of 8th and 9th: \(\frac{53 + 67}{2} = 60\)

Q1: median of first 8 numbers (positions 1 - 8): 1:20, 2:24, 3:27, 4:39, 5:41, 6:44, 7:49, 8:53. Median of these 8 is average of 4th and 5th: \(\frac{39 + 41}{2} = 40\)

Q3: median of last 8 numbers (positions 9 - 16): 9:67, 10:75, 11:84, 12:97, 13:103, 14:108, 15:111, 16:120. Median of these 8 is average of 12th and 13th? Wait no, 8 numbers: positions 9 - 16 (8 numbers). So median is average of 12th and 13th? Wait 9:67 (1), 10:75 (2), 11:84 (3), 12:97 (4), 13:103 (5), 14:108 (6), 15:111 (7), 16:120 (8). So median of these 8 is average of 4th and 5th: \(\frac{97 + 103}{2} = 100\)

Maximum: \(120\)

So the five - number summary is: Min = 20, Q1 = 40, Median = 60, Q3 = 100, Max = 120.

Now let's analyze the box - plots:

First box - plot: The left whisker starts at 20, Q1 is at 40, median at 60, Q3 at 100, right whisker at 120.

Second box - plot: Let's check the Q3. If Q3 is not 100, but let's see the first box - plot's Q3 is at 100, median at 60, Q1 at 40. Which matches our five - number summary.

Answer:

The first box - plot (the one with the box from 40 to 100, median at 60, whiskers from 20 to 120)