Understanding Box and Whisker Plots
Introduction
- Box and whisker plots, also known as box plots, are a method for displaying data and understanding its distribution.
- Initially, they may seem complex, but they provide a visual representation of data spread.
Purpose
- Box plots show a five-number summary:
- Minimum
- First quartile (Q1)
- Median (Second quartile, Q2)
- Third quartile (Q3)
- Maximum
- They help in understanding the distribution and variability of data.
Example: Years of Teaching Experience
- Data: Survey of 10 teachers' years of teaching experience.
- Data is ordered from least to greatest.
Parts of a Box and Whisker Plot
-
Minimum and Maximum
- Minimum: Smallest data point
- Maximum: Largest data point
- In the example, minimum is 3 years, maximum is 18 years.
- These are represented by the ends of the "whiskers."
-
Median (Q2)
- Line inside the box represents the median or the 50th percentile.
- For 10 data points, median is calculated as the average of the 5th and 6th values.
- Example median: 9 (average of 8 and 10).
-
First Quartile (Q1) - Lower Quartile
- Median of the lower half of the data set.
- Represents the 25th percentile.
- Example Q1: 7.
-
Third Quartile (Q3) - Upper Quartile
- Median of the upper half of the data set.
- Represents the 75th percentile.
- Example Q3: 12.
-
Interquartile Range (IQR)
- The box represents the IQR, covering the middle 50% of the data between Q1 and Q3.
Distribution of Data
- Data is divided into four parts:
- Each quartile represents approximately 25% of the data.
- Whiskers show the spread outside the interquartile range, to the minimum and maximum.
Recap
- Key components: Minimum, Q1, Median, Q3, Maximum.
- Data spread visualization: Box shows IQR, whiskers show overall range.
Conclusion
- Understanding box and whisker plots helps in visualizing data distribution effectively.
- Helpful for identifying spread, center, and variability in data sets.
Tip: Whenever you have two numbers and need to find the median between them, take their average.