To draw a box and whisker plot for the data set 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19, we first need to follow several steps:
- Order the Data: Arrange the numbers in ascending order:
- 19, 20, 20, 21, 21, 25, 25, 26, 28, 28, 29, 29, 30, 32, 35, 35, 35, 36
- Determine the Five-Number Summary: This includes:
- Minimum: The smallest number, which is 19.
- First Quartile (Q1): The median of the first half of the data. For our dataset, Q1 is 25.
- Median (Q2): The middle number of the data set. With 18 values, the median is the average of the 9th and 10th values (28 and 28), so Q2 is 28.
- Third Quartile (Q3): The median of the second half of the data, which is 35.
- Maximum: The largest number, which is 36.
- Draw the Box-and-Whisker Plot: Use these five statistics to plot the box:
- Draw a number line that covers the range of your data (from 19 to 36).
- Draw a box from Q1 (25) to Q3 (35).
- Inside the box, draw a line at the median (28).
- Extend a ‘whisker’ from the minimum (19) to Q1 (25), and another whisker from Q3 (35) to the maximum (36).
Visualizing this data with a box and whisker plot helps you quickly see the distribution, including the median, quartiles, and potential outliers, providing valuable insights into the data set.