15.3. Five Number Summary http://www.ck12.org
Example B
Compute the five number summary for the following data:
4, 8, 11, 11, 12, 14, 16, 20, 21, 25
Solution:There are 10 observations total.
- Lowest value (minimum) : 4
- Q1 : 11(Note that this is the median of the first half of the data - 4, 8, 11, 11, 12)
- Q2 :^12 + 214 = 13 (Note that this is the median of the full set of data)
- Q3 : 20(Note that this is the median of the second half of the data - 14, 16, 20, 21, 25)
- Upper value (maximum) : 25
Example C
Compute the five number summary for the following data:
3, 7, 10, 14, 19, 19, 23, 27, 29
Solution:There are 9 observations total. To calculateQ1 andQ3, you should include the median in both the lower
half and upper half calculations.
- Lowest value (minimum) : 3
- Q1 : 10(this is the median of 3, 7, 10, 14, 19)
- Q2 : 19
- Q3 : 23(this is the median of 19, 19, 23, 27, 29)
- Upper value (maximum) : 29
Concept Problem Revisited
To compute the five number summary, it helps to order the data.
0, 0, 1, 2, 13, 27, 61, 63
- Since there are 8 observations, the median is the average of the 4thand 5thobservations:^2 + 213 = 7. 5
- The lowest observation is 0.
- The highest observation is 63.
- The middle of the lower half is^0 + 21 = 0. 5
- The middle of the upper half is^27 + 261 = 44
The five number summary is 0, 0.5, 7.5, 44, 63
Vocabulary
Therankof an observation is the number of observations that are less than or equal to the value of that observation.
Data is divided into four parts by the first quartile(Q 1 ), second quartile(Q 2 )and third quartile(Q 3 ). The
second quartileis also known as the median.
Guided Practice
- Create a set of data that meets the following five number summary:
{2, 5, 9, 18, 20} - Compute the five number summary for the following data: