Question

Problem
The data below represents the number of practices each member of Nidhi's ski team attended.
\[25\],
\[28\],
\[29\],
\[29\],
\[30\],
\[34\],
\[35\],
\[35\],
\[37\],
\[38\]
Which box plot correctly summarizes the data?
Choose 1 answer:
Choose 1 answer:
(Choice A) A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 30. The right whisker extends from 35 to 38. All values estimated.
A
A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 30. The right whisker extends from 35 to 38. All values estimated.
(Choice B) A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 32. The right whisker extends from 35 to 38. All values estimated.
B
A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 32. The right whisker extends from 35 to 38. All values estimated.
(Choice C) A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 34. The right whisker extends from 35 to 38. All values estimated.
C
A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 34. The right whisker extends from 35 to 38. All values estimated.
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Answer 1

To create a box plot, we need to determine the five-number summary of the dataset, which consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

The data set provided is:
\[25, 28, 29, 29, 30, 34, 35, 35, 37, 38\]

1. **Minimum**: The smallest value is 25.
2. **Maximum**: The largest value is 38.
3. **Median (Q2)**: Since there are 10 values, the median will be the average of the 5th and 6th values. The 5th value is 30 and the 6th value is 34, so:
\[
Q2 = \frac{30 + 34}{2} = 32
\]
4. **First Quartile (Q1)**: This is the median of the first half of the data (the first 5 values: 25, 28, 29, 29, 30). The 3rd value here is 29, so:
\[
Q1 = 29
\]
5. **Third Quartile (Q3)**: This is the median of the second half of the data (the last 5 values: 34, 35, 35, 37, 38). The 3rd value here is 35, so:
\[
Q3 = 35
\]

Now we have the five-number summary:
- Minimum: 25
- Q1: 29
- Q2 (Median): 32
- Q3: 35
- Maximum: 38

Now let's evaluate the box plots provided in the choices:

- **Choice A**: Left whisker from 25 to 29 (correct), box from 29 to 35 (correct), median at 30 (incorrect, should be at 32), right whisker from 35 to 38 (correct).
- **Choice B**: Left whisker from 25 to 29 (correct), box from 29 to 35 (correct), median at 32 (correct), right whisker from 35 to 38 (correct).
- **Choice C**: Left whisker from 25 to 29 (correct), box from 29 to 35 (correct), median at 34 (incorrect, should be at 32), right whisker from 35 to 38 (correct).

Based on this analysis:
**The correct choice is (Choice B)**, which shows the median correctly positioned at 32.