Box Plots

 

What Is a Box Plot?

A box plot (also known as a box-and-whisker diagram) is a visual way of showing the spread and distribution of a data set.

It uses five key values to summarise the data:

• Minimum (lowest value)
• Lower quartile (Q1) – 25% of the data is below this value
• Median (Q2) – the middle value
• Upper quartile (Q3) – 75% of the data is below this value
• Maximum (highest value)

 

 

The plot helps identify:

• The central tendency (median)
• The spread (range and interquartile range)
• Any asymmetry in the data

 

How Do I Draw a Box Plot?

Step-by-Step:

1. Plot five vertical lines:
   • One at each of the five values: min, Q1, median, Q3, max.
2. Draw the box:
   • The box spans from Q1 to Q3.
   • A line is drawn inside the box for the median.
3. Add the whiskers:
   • These are horizontal lines that extend from the minimum to Q1, and from Q3 to the maximum.

The box represents the middle 50% of the data.

The whiskers represent the bottom and top 25%.

 

Interpreting a Box Plot

• The wider the box, the greater the spread in the middle 50%.
• If the median is closer to Q1, the data is skewed right (positively skewed).
• If the median is closer to Q3, the data is skewed left (negatively skewed).
• If a whisker is longer, that part of the data is more spread out.

 

Comparing Two Box Plots

When comparing, mention:

1. Averages (medians)
   • Which group has a higher median?
   • What does that mean in the real-world context?
2. Spread (IQR or range)
   • Which group has a more consistent set of data (smaller IQR)?
   • What does that suggest?

 

Example

Two sports teams, Team X and Team Y, track the number of training hours completed each week.

Team X's box plot is already drawn.

 

 

Team Y’s data is as follows:

 

Statistic	Value
Minimum	6
Lower Quartile	7.5
Median	9
Upper Quartile	11.5
Maximum	13

 

(a) Draw the box plot for Team Y

• Mark the five vertical lines at 6, 7.5, 9, 11.5, and 13.
• Draw the box from 7.5 to 11.5.
• Draw a line at the median (9).
• Add whiskers from 6 to 7.5 and from 11.5 to 13.

 

 

(b) Compare the two teams’ training habits

 

 

Medians:

Team Y has a higher median training time (9 hours) compared to Team X (8 hours).

This means Team Y trains more on average each week.

Spread:

Team Y has a larger IQR (11.5 - 7.5 = 4) compared to Team X (9.5 - 7 = 2.5).

This suggests Team X is more consistent in how many hours they train each week.