The median on a box plot is represented by the vertical line that divides the box into two parts.
Here's a breakdown of how to identify the median and what the other components of a box plot represent:
Understanding Box Plots
A box plot (also known as a box-and-whisker plot) visually represents the distribution of a dataset through its quartiles. It displays the following key values:
- Minimum: The smallest data point in the set (excluding outliers). Represented by the far left end of the whisker.
- First Quartile (Q1): The median of the lower half of the data. Represents the left edge of the box.
- Median (Q2): The middle value of the entire dataset. Represented by the vertical line inside the box.
- Third Quartile (Q3): The median of the upper half of the data. Represents the right edge of the box.
- Maximum: The largest data point in the set (excluding outliers). Represented by the far right end of the whisker.
- Outliers: Data points that fall significantly outside the overall pattern of the data. Shown as individual points beyond the whiskers.
Identifying the Median
To find the median on a box plot, simply locate the vertical line within the box. This line indicates the central tendency of your data:
- The vertical line inside the box = The Median (Q2)
Example
Imagine a box plot representing test scores. The box extends from 70 (Q1) to 90 (Q3), and the vertical line representing the median is at 80. This tells you that half of the students scored below 80, and half scored above 80. The whiskers extend to the minimum score of 60 and the maximum score of 100.
Additional Information
Sometimes, a box plot may also indicate the mean (average) of the data with a dot or a cross within the box. This can be useful for comparing the mean and median and understanding the skewness of the data. If the median is to the left of the mean, the data is skewed right (positively skewed), and if the median is to the right of the mean, the data is skewed left (negatively skewed).
