Question

Construct a box-and-whisker plot for the data with a minimum of 12, first quartile of 15.5, median of 17, third quartile of 18.5, and a maximum of 22. Solve for the interquartile range. Upload your plot for your teacher to review.

Answer 1

To construct a box-and-whisker plot, plot the minimum, Q1, median, Q3, and maximum on a number line and draw a box from Q1 to Q3 with 'whiskers' to the minimum and maximum. The interquartile range (IQR) for the provided data is 3.

Step-by-step explanation:

To construct a box-and-whisker plot, also known as a box plot, you need five key values: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. For the given data, these are 12, 15.5, 17, 18.5, and 22, respectively.

1. Draw a number line that includes the smallest and largest values of your data set.
2. Mark the minimum value (12) and the maximum value (22) on the number line.
3. Draw a box from the first quartile (15.5) to the third quartile (18.5).
4. Within this box, draw a line at the median value (17).
5. Draw 'whiskers' from the ends of the box to the minimum and maximum values.

To calculate the interquartile range (IQR), subtract the first quartile from the third quartile:

IQR = Q3 - Q1

IQR = 18.5 - 15.5

IQR = 3

The interquartile range is 3, indicating the range of the middle 50% of the data.