The problem gives a data set representing the number of baby teeth lost by each student in Ms. Armstrong's third-grade class. The data set is: $5, 9, 5, 3, 7, 5, 6, 5, 3, 9, 8, 8, 6, 10, 7, 4$. We need to determine which of the two given box plots correctly represents this data.

1. Problem Description

The problem gives a data set representing the number of baby teeth lost by each student in Ms. Armstrong's third-grade class. The data set is: $5, 9, 5, 3, 7, 5, 6, 5, 3, 9, 8, 8, 6, 10, 7, 4$.

We need to determine which of the two given box plots correctly represents this data.

2. Solution Steps

To determine the correct box plot, we need to find the following values from the data set:

Minimum, First Quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum.

First, we sort the data set in ascending order:

$3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10$

Minimum: The smallest value in the data set is $3$.

Maximum: The largest value in the data set is $10$.

Median (Q2): Since there are 16 data points (an even number), the median is the average of the 8th and 9th values. In the sorted data, the 8th value is 6 and the 9th value is 6, so the median is $\frac{6+6}{2} = 6$.

First Quartile (Q1): Q1 is the median of the lower half of the data. The lower half of the data is $3, 3, 4, 5, 5, 5, 5, 6$. Since there are 8 data points in the lower half, Q1 is the average of the 4th and 5th values. In the lower half, the 4th value is 5 and the 5th value is 5, so $Q1 = \frac{5+5}{2} = 5$.

Third Quartile (Q3): Q3 is the median of the upper half of the data. The upper half of the data is $6, 7, 7, 8, 8, 9, 9, 10$. Since there are 8 data points in the upper half, Q3 is the average of the 4th and 5th values. In the upper half, the 4th value is 8 and the 5th value is 8, so $Q3 = \frac{8+8}{2} = 8$.

Therefore, we have:

Minimum = 3

Q1 = 5

Median = 6

Q3 = 8

Maximum = 10

Now, we compare these values to the two box plots.

The first box plot has the following characteristics:

Minimum: approximately 3.5

Q1: approximately 5

Median: approximately 7.5

Q3: approximately 8

Maximum: approximately 10

The second box plot has the following characteristics:

Minimum: approximately 3.5

Q1: approximately 5

Median: approximately 6

Q3: approximately 8

Maximum: approximately 9.5

The second box plot is closer to our calculated values.

3. Final Answer

The second box plot represents the data.