01 Key Concepts
Five-Number Summary
Minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum — the five values a box plot displays.
Quartiles
Q1 is the median of the lower half of the data; Q3 is the median of the upper half. Together with the median, they divide the data into four equal parts.
Interquartile Range (IQR)
IQR = Q3 - Q1, representing the spread of the middle 50% of the data.
The Box and Whiskers
The box spans from Q1 to Q3; a line inside marks the median. Whiskers extend to the minimum and maximum, excluding outliers.
Identifying Outliers
A common rule: any value below Q1 - 1.5*IQR or above Q3 + 1.5*IQR is flagged as an outlier and plotted separately.
02 Key Formulas
- IQR = Q3 - Q1
- Outlier bounds: below Q1 - 1.5*IQR or above Q3 + 1.5*IQR
03 Solved Examples
Example 1 Find the five-number summary of 2, 4, 6, 8, 10, 12, 14.
- Minimum = 2, Maximum = 14.
- Median (middle of 7 values) = 8.
- Lower half (below median): 2,4,6; Q1 = median of these = 4.
- Upper half (above median): 10,12,14; Q3 = median of these = 12.
Answer: Min=2, Q1=4, Median=8, Q3=12, Max=14
Example 2 Find the IQR for the dataset above.
- IQR = Q3 - Q1 = 12 - 4.
Answer: IQR = 8
Example 3 Using Q1=4 and Q3=12 (IQR=8), determine the outlier boundary values.
- Lower bound = Q1 - 1.5*IQR = 4 - 1.5*8 = 4 - 12 = -8.
- Upper bound = Q3 + 1.5*IQR = 12 + 1.5*8 = 12 + 12 = 24.
Answer: Any value below -8 or above 24 would be an outlier
04 Practice Questions
1What five values make up the five-number summary?
Minimum, Q1, median, Q3, maximum
2Find the IQR if Q1=10 and Q3=25.
15
3What does the 'box' in a box plot represent?
The middle 50% of the data, from Q1 to Q3
4What do the 'whiskers' typically extend to?
The minimum and maximum values, excluding outliers
5If Q1=20, Q3=40, find the upper outlier bound.
40 + 1.5*20 = 70
📄 Box Plots — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.