To draw a box and whisker plot (also known as a whisker plot) for the given data set, you’ll want to follow the steps outlined below:
- Collect Data: Start with the data points: 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19.
- Sort the Data: Rank the data 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:
- Minimum: The smallest value is 19.
- First Quartile (Q1): The median of the first half of the data is 25.
- Median (Q2): The median of the entire data set is 28.
- Third Quartile (Q3): The median of the second half of the data is 35.
- Maximum: The largest value is 36.
- Plot the Box:
- Draw a number line that accommodates the range of your data.
- Plot the first quartile (Q1), median (Q2), and third quartile (Q3) as vertical lines.
- Draw a box from Q1 to Q3, with the median line inside the box.
- Add Whiskers:
- Extend lines (whiskers) from the edges of the box (Q1 and Q3) to the minimum and maximum values, respectively.
- Whiskers should not exceed 1.5 times the interquartile range (IQR). If they do, you can plot outliers as individual points.
- Identify Outliers:
- To find outliers, calculate the IQR: Q3 – Q1 = 35 – 25 = 10.
- Determine lower and upper bounds for outliers: Lower Bound = Q1 – 1.5 * IQR = 25 – 15 = 10; Upper Bound = Q3 + 1.5 * IQR = 35 + 15 = 50.
- All data points in range (19, 36) are within bounds, so there are no outliers.
In conclusion, you will have a box and whisker plot that clearly illustrates the distribution of your data. It provides a visual representation of the median, quartiles, and any potential outliers, making it an excellent tool for data analysis and comparison.