To determine which box plot correctly summarizes the data, let's go through the process of creating a box plot step by step.

Step 1: Organize the Data

The data set is: $25, 28, 29, 29, 30, 34, 35, 35, 37, 38$

Step 2: Calculate Key Statistics

To make a box plot, we need the following five statistics:

1. Minimum: The smallest value in the dataset, which is 25.
2. First Quartile (Q1): The median of the lower half of the data.
   • Lower half of the data: $25, 28, 29, 29, 30$
   • The median of this subset is 29, so $Q1 = 29$.
3. Median (Q2): The median of the entire dataset.
   • The full dataset: $25, 28, 29, 29, 30, 34, 35, 35, 37, 38$
   • The median is the average of the two middle values: $\frac{30 + 34}{2} = 32$, so $Q2 = 32$.
4. Third Quartile (Q3): The median of the upper half of the data.
   • Upper half of the data: $34, 35, 35, 37, 38$
   • The median of this subset is 35, so $Q3 = 35$.
5. Maximum: The largest value in the dataset, which is 38.

Step 3: Create the Box Plot

From the data:

• The minimum is 25.
• The first quartile is 29.
• The median is 32.
• The third quartile is 35.
• The maximum is 38.

Now, let’s review the boxplot choices:

• Choice A has a vertical line at 34 (which is incorrect, as the median is 32).
• Choice B has a vertical line at 30 (which is incorrect, as the median is 32).
• Choice C has a vertical line at 32 (which is correct, as the median is 32).

Conclusion:

The correct box plot is Choice C.

Let me know if you'd like more details on this process or have any questions!

Related questions:

1. How do you calculate the quartiles for an odd number of data points?
2. What is the difference between the first and third quartile?
3. How can you find the median in a dataset with an even number of data points?
4. How does the interquartile range (IQR) help in identifying outliers in a dataset?
5. What is the significance of the whiskers in a box plot?

Tip:

To avoid errors when reading box plots, always double-check that the vertical line inside the box correctly matches the median of your dataset!