What is a Five Number Summary? (With Examples)

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The five-number summary for a given set of data is a set of 5 representative numerical values obtained from the data which gives us an idea of how the data looks like and how it is distributed.

The main advantage of the 5-number summary is that instead of tediously going through the entire data we can use it to get an overview of the data at just a glance.

The 5-number summary consists of the following 5 pieces of information:

1. The smallest value.
2. The lower quartile (the value beneath which 25% of data values lie).
3. The median (the value beneath which 50% of the data values lie).
4. The lower quartile (the value beneath which 75% of data values lie).
5. The highest value

Some outliers in the data may also be included in the five-number summary. This is because it contains the highest and lowest values which may turn out to be outliers.

How to calculate the five-number summary?

The procedure to calculate the five-number summary is to simply arrange our data from highest to lowest and then find the median and the lower and upper quartiles.

A five-number summary is sometimes visualized using a box plot with “whiskers” attached to it.

Example:

Calculate the five-number summary for the given set of data:

1, 3, 4, 17, 19, 21, 45, 77, 79.

Solution:

As the data is already in ascending order we clearly see that the highest and lowest values are 84 and 1 respectively.

We have N=9 observations in the given data.

Median= (N/2)th term = 4.5th term, that is the 5th term = 19

Lower quartile= (N/4)th term = 2.25th term, that is the 2nd term = 3

Upper quartile= (3N/4)th term = 6.75th term, that is the 7th term = 45.

So our five-number summary for the data is,

1 – 3 – 19 – 45 – 84.

Seven Number Summary:

Sometimes if a person desires to obtain more information about the data they use the “seven summary summary”.

The 7-number summary consists of the 2nd, 9th, 25th, 50th, 75th, 91st, and 98th percentiles and gives us a much more accurate picture as compared to the five-number summary.