Third Quartile
High Quartile
Higher Quartile
Q3
For a set of data, a number for which 75% of the
data is less than that number. The third quartile is the same as
the median of
the part of the data which is greater than the median. Same as
75th percentile.
See
also
First quartile, five-number summary
Worked Example
Problem: Find the third quartile (Q3) of this data set: 3, 7, 8, 12, 15, 18, 21, 24, 30.
Step 1: Arrange the data in order (already done) and find the median. There are 9 values, so the median is the 5th value.
Median=15 Step 2: Identify the upper half of the data — all values above the median. Do not include the median itself when the data set has an odd number of values.
Upper half: 18,21,24,30 Step 3: Find the median of the upper half. There are 4 values, so average the 2nd and 3rd values.
Q3=221+24=22.5 Answer: The third quartile is Q3 = 22.5. This means 75% of the data values (roughly 7 out of 9) fall below 22.5.
Another Example
Problem: Find Q3 for the data set: 5, 10, 14, 18, 22, 26.
Step 1: The data is already sorted. There are 6 values (even count), so the median lies between the 3rd and 4th values.
Median=214+18=16 Step 2: The upper half consists of the three values above the median position: 18, 22, 26.
Upper half: 18,22,26 Step 3: The median of these three values is the middle one.
Answer: The third quartile is Q3 = 22.
Frequently Asked Questions
How do you find Q3 on a calculator or by hand?
Sort the data from least to greatest, find the overall median, then look at only the values above that median. Q3 is the median of that upper half. Most graphing calculators compute Q3 automatically under their one-variable statistics function (often listed as 1-Var Stats).
Is Q3 the same as the 75th percentile?
Yes. Q3 and the 75th percentile both represent the value below which 75% of the data falls. The terms are interchangeable in standard usage, though some advanced methods for computing percentiles can give slightly different results for small data sets.
First Quartile (Q1) vs. Third Quartile (Q3)
Q1 marks the 25th percentile — the median of the lower half of the data — while Q3 marks the 75th percentile — the median of the upper half. Together they define the interquartile range (IQR = Q3 − Q1), which measures the spread of the middle 50% of the data. Q1 tells you where the lower quarter ends; Q3 tells you where the upper quarter begins.
Why It Matters
Q3 is essential for constructing box plots (box-and-whisker diagrams), where it forms the right edge of the box. It is also used to calculate the interquartile range and to identify outliers — any data point above Q3 + 1.5 × IQR is typically flagged as an outlier. In real-world contexts like standardized testing or salary data, Q3 tells you the threshold above which only the top 25% of values lie.
Common Mistakes
Mistake: Including the overall median in the upper half when the data set has an odd number of values.
Correction: When the total count is odd, exclude the median value before finding Q3. The upper half should contain only the values strictly above the median's position.
Mistake: Forgetting to sort the data before finding quartiles.
Correction: Quartiles depend on the ordered position of values. Always arrange the data from smallest to largest before identifying the median or any quartile.
