Every box plot has exactly 5 number summary. Memorize this order left → right on the number line!
Minimum
Q1 (Lower Quartile)
Median (Q2)
Q3 (Upper Quartile)
Maximum
Look at the box plot above. What is the Interquartile Range (IQR)?
In a box plot, which value does the line INSIDE the box always represent?
The whiskers reach from Min to Max. The box holds Q1 to Q3.
Each section (left whisker / left box / right box / right whisker) contains about 25% of data.
Test scores: 12, 18, 22, 25, 28, 31, 35, 40, 45, 50
Five-Number Summary: Min = 12 Q1 = 22 Median = 29.5 Q3 = 40 Max = 50
Using the example data above, what is the Range of the data set?
What percentage of the data falls between Q1 and Q3 (inside the box)?
A data set has Min = 5, Q1 = 12, Median = 20, Q3 = 28, Max = 40.
⚠️ TRICKY: How long is the right whisker?
If the box in a box plot is very wide, it tells us the middle 50% of the data is...
Step 1: Sort data from smallest to largest.
Step 2: Find the overall Median (middle value).
Step 3: Split data into lower half & upper half — find Q1 (median of lower) & Q3 (median of upper).
Data: 7, 3, 9, 1, 5, 11, 4
① Sort: 1, 3, 4, 5, 7, 9, 11 → Median = 5
② Lower half: 1, 3, 4 → Q1 = 4
③ Upper half: 7, 9, 11 → Q3 = 9
④ Summary: Min=1, Q1=4, Median=5, Q3=9, Max=11 | IQR = 9−4 = 5
Find the Median of: 8, 3, 15, 7, 12, 1, 10
Find the IQR of this data set: 4, 6, 8, 10, 12, 14, 16
⚠️ Even number of values!
Find the Median of: 3, 7, 8, 12, 15, 20
Data set: 2, 5, 6, 9, 11, 14, 18, 22
What is Q1?
(Hint: lower half = first 4 values)
Left-skewed (negative): Long left whisker → most data bunched on the RIGHT.
Right-skewed (positive): Long right whisker → most data bunched on the LEFT.
Symmetric: Box sits in the middle; both whiskers about equal length.
A box plot has a very long right whisker. This means the distribution is...
⚠️ Common mistake!
Class A: Median = 72. Class B: Median = 68.
Which class has the higher typical score?
Two classes took the same test:
Class A — IQR = 30 | Class B — IQR = 8
Which class has more consistent scores?
Box Plot A: Min=10, Q1=20, Median=30, Q3=40, Max=50
Box Plot B: Min=10, Q1=25, Median=30, Q3=35, Max=50
⚠️ They have the same median AND same range!
Which plot shows more spread in the middle 50%?
Any value below (Q1 − 1.5 × IQR) or above (Q3 + 1.5 × IQR) is an outlier.
On a box plot, outliers are shown as individual dots outside the whiskers.
Q1 = 10, Q3 = 20 → IQR = 10
Lower fence: 10 − 1.5(10) = 10 − 15 = −5
Upper fence: 20 + 1.5(10) = 20 + 15 = 35
Any value below −5 or above 35 is an outlier.
Is 40 an outlier? → 40 > 35 → YES ✓
Q1 = 15, Q3 = 35. IQR = 20.
What is the upper fence (upper outlier boundary)?
⚠️ Full outlier test!
Data: Q1=12, Q3=24, IQR=12. A value of 45 is in the data.
Is 45 an outlier?
⚠️ Range vs IQR confusion!
A box plot: Min=5, Q1=15, Median=25, Q3=35, Max=80.
What is the Range? What is the IQR?
⚠️ Median ≠ Mean!
Box plot shows Median = 50. A student says "the average is 50." Is this correct?
⚠️ Reading percentages!
A box plot: Min=10, Q1=30, Median=50, Q3=70, Max=90.
Approximately what percent of data is above 70?
⚠️ BOSS LEVEL! Combining everything.
Data: 2, 4, 4, 6, 8, 10, 12, 14, 16, 100
After finding the 5-number summary and checking for outliers, which value is an outlier?
(Sorted: Q1=5, Q3=13, IQR=8)
📝 My Notes & Observations