To determine the most appropriate scale for the number line on the box-and-whisker plot, we need to consider the range of the given data set.

The data set is:
27, 14, 46, 38, 32, 18, 21.

First, let's find the minimum and maximum values in the data set:

• Minimum value: 14
• Maximum value: 46

Now, let's evaluate each option:

1. 10 to 50: This range includes all the data points (minimum 14, maximum 46) and provides a little extra space on both ends, which is a reasonable choice.
2. 20 to 50: This range also includes all the data points, but it leaves out the smallest value (14), so it is not ideal.
3. 0 to 40: This range doesn’t cover the maximum value (46), so it’s not appropriate.
4. 0 to 100: This range is much broader than needed, and it wastes space, so it's not ideal.

Conclusion:

The most appropriate scale would be 10 to 50, as it comfortably includes the entire data set and leaves a little extra space.

Would you like further details or have any questions on how to construct the box-and-whisker plot?

Here are some related questions you might find helpful:

1. How do you calculate the median, quartiles, and interquartile range for a set of data?
2. What is the purpose of a box-and-whisker plot?
3. How do you determine the outliers in a data set using a box-and-whisker plot?
4. What is the formula for the interquartile range (IQR)?
5. How do you identify the five-number summary from a box-and-whisker plot?

Tip: When choosing a scale for a box-and-whisker plot, ensure it covers the entire range of your data and provides some room for clarity at both ends of the number line.