http://www.ck12.org Chapter 15. Concepts of Statistics
15.3 Five Number Summary
Here you will calculate quartiles and produce five number summaries for data sets.
When given a long list of numbers, it is useful to summarize the data. One way to summarize the data is to give the
lowest number, the highest number and the middle number. In addition to these three numbers it is also useful to
give the median of the lower half of the data and the median of the upper half of the data. These five numbers give a
very concise summary of the data.
What is the five number summary of the following data?
0, 0, 1, 2, 63, 61, 27, 13
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MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/62539http://www.youtube.com/watch?v=XDS5TgZ4CJA The 5 Number Summary
Guidance
Suppose you have ordered data withmobservations. The rank of each observation is shown by its index.
y 1 ≤y 2 ≤y 3 ≤···≤ym
In data sets that are large enough, you can divide the numbers into four parts called quartiles. The quartiles of interest
are the first quartile,Q1, the second quartile,Q2, and the third quartileQ3. The second quartile,Q2, is defined to
be the median of the data. The first quartile,Q1, is defined to be the median of the lower half of the data. The third
quartile,Q3, is similarly defined to be the median of the upper half of the data.
These three numbers in addition to the minimum and maximum values are the five number summary. Note that there
are variations of the five number summary that you can study in a statistics course.
Example A
Compute the five number summary for the following data.
2, 7, 17, 19, 25, 26, 26, 32
Solution:There are 8 observations total.
- Lowest value (minimum) : 2
- Q1 :^7 + 217 = 12 (Note that this is the median of the first half of the data - 2, 7, 17, 19)
- Q2 :^19 + 225 = 22 (Note that this is the median of the full set of data)
- Q3 : 26(Note that this is the median of the second half of the data - 25, 26, 26, 32)
- Upper value (maximum) : 32