What a five-number summary is
A five-number summary describes a data set using five values: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. These values help show the center and spread of the data.
How to find it
- Order the data from least to greatest.
- Find the minimum and maximum: the smallest and largest values.
- Find the median: the middle value of the ordered list.
- If there is an odd number of data values, the median is the single middle value.
- If there is an even number, the median is the average of the two middle values.
- Find Q1 and Q3:
- Q1 is the median of the lower half of the data.
- Q3 is the median of the upper half of the data.
- When the data set has an odd number of values, do not include the median in either half.
- Write the summary in order: minimum, Q1, median, Q3, maximum.
Check your work
- Make sure the numbers are in increasing order.
- The five values should satisfy: minimum ≤ Q1 ≤ median ≤ Q3 ≤ maximum.
- If the exercise asks for a simplified answer, reduce any averages to simplest form.
Tip
If you are unsure about Q1 and Q3, split the ordered list into two halves carefully before finding their medians.