**The Five-Number Summary**

The five-number summary is five-point scale that we can use to summarise the information about a data set. The five-number summary contains:

● Minimum value

● First or lower quartile: 25% of the data lies below the first quartile

● Median: 50% of the data lies below and above the median

● Third or upper quartile: 25% of the data lies above the third quartile

● Maximum Value

Example 1

Consider the following values

The first thing to do when confronted with a new set of data is to arrange it in ascending order:

● Range =14-2=12

● Minimum value =2

● First quartile

*Q*

_{1}=

*T*

_{7}=5 (For discrete data: 0.25×27=6.75 thus 7th term)

● Median =8

● Third quarti1e

*Q*

_{3}=

*T*

_{21}=9 (For discrete data: 0.75×26=20.25 thus 21st term)

● Maximum Value =14

● Inter-quartile range =9-5=4

● Semi-inter-quartile range

Question 1

Linda has worked as a florist for nine months. She sold the following number of wedding bouquets:

{16; 14; 8; 12; 6; 5; 3; 5; 7}

Give the five number summary of Linda’s sales.

solution:

We first order the data set.

{3; 5; 5; 6; 7; 8; 12; 14; 16}

Now we can read off the minimum as the first value (3) and the maximum as the last value (16).

Next we need to determine the quartiles.

There are 9 values in the data set. Using the percentile formula, we can determine that the median lies at the fifth value, making it 7.

The first quartile lies at the third value, making it 5.

The third quartile lies at the seventh values, making it 12. The five number summary is:

Minimum: 3

*Q*_{1}: 5

Median: 7

*Q*_{3}: 12

Maximum: 16