Question

The box plot represents this data set.

16, 16, 16, 18, 18, 20, 24, 28, 30, 34

What value does the letter A represent on the box plot of the data?

Enter your answer in the box.

A number line with a box in the middle

Answer 1

To determine what value the letter A represents on the box plot for the given data set \(16, 16, 16, 18, 18, 20, 24, 28, 30, 34\), we need to identify key statistics: the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

1. **Minimum value**: 16
2. **Maximum value**: 34
3. **Median (Q2)**: The median is the middle value. For 10 data points, the median will be the average of the 5th and 6th values.
\[
\text{Median} = \frac{18 + 20}{2} = 19
\]
4. **First Quartile (Q1)**: This is the median of the first half of the data (the first 5 numbers):
- Data for Q1: \(16, 16, 16, 18, 18\)
- Median of these values is 16 (the third value).
5. **Third Quartile (Q3)**: This is the median of the second half of the data (the last 5 numbers):
- Data for Q3: \(20, 24, 28, 30, 34\)
- Median of these values is 28 (the third value).

Now we summarize the values:
- Minimum: 16
- Q1: 16
- Median (Q2): 19
- Q3: 28
- Maximum: 34

Assuming that A represents a specific position on the box plot, it typically would refer to the position of Q1, the median, or Q3 depending on what label A corresponds to. Based on common usage, A is most likely to be representing the first quartile (Q1).

Thus, the value that A represents on the box plot is:
\[
\boxed{16}
\]