Statistics is the study of data. It deals with collection, interpretation, organization and analysis of data. To summarize a data set five number summary is used, which tells about the minimum, Q1, median, Q3 and maximum values of the data set. |

**• Minimum :**The lowest value in the data set.

**• Q1 :**First quartile is the median of the lower half.

**• Median :**The middle value of the data set.

**• Q3 :**Third quartile is the median of the upper half.

**• Maximum :**The highest value of the data set.

**1)**Arrange all the numbers in the ascending order.

**2)**The leftmost element is the minimum and the rightmost is the maximum.

**3)**The element exactly in the middle of the ordered data is the median. If numbers of observation is even, median is the average of the two middle elements.

**4)**The median of the data from the minimum element to the element just left of the median is Q1.

**5)**The median of the data from the element just right of the median and the maximum element is Q3.

**Example 1:**

List the five-number summary when the marks by 8 schools students in a physics exam are as follows. 99, 77, 79, 86, 80, 87, 94, 87 out of 100.

**Solution:**

Given 99,77,79,86,80,87,94,87 out of 100

First arranging the marks.

77, 79, 80, 86, 87, 87, 94, 99

which is 77

Find the maximum marks

which is 99

= $86.5$

First quartile is,

$Q_{3}$ = $\frac{87+94}{2}$ = $90.5$

Min, $Q_{1}$, $Q_{2}$, $Q_{3}$, Max

77, 79.5, 86.5, 90.5, 99

**Example 2:**

Evaluate five-number summary for below given data.

8, 5, 8, 9, 3, 0, 6, 1, 4, 6, 8, 6, 9.

**Solution:**

Given 8, 5, 8, 9, 3, 0, 6, 1, 4, 6, 8, 6, 9

First arrange the given data,

The minimum of the data is 0

The maximum of the data is 9

The lower half part = 0, 1, 3, 4, 5, 6

The Lower quartile is,

$Q_{3}$ = $\frac{8+8}{2}$ = 8

Hence five-number summary is for given data is

Min, $Q_{1}$, $Q_{2}$, $Q_{3}$, Max

0, 3.5, 6, 8, 9