Upper Quartile

Introduction to Upper quartile:
In descriptive, a quartile statistics is any of the three values which divide the sorted data set into four equal parts .There are three quartile in the data set.

Lower Quartile (First Quartile)
Median (Second Quartile)
Upper quartile(Third Quartile)


Upper Quartile:

In the quartile, the 25 % of data which lie at the top of the data set is called as upper quartile.We can also define it as the middle value of the upper half of the data set.

21, 5, 22, 33, 17, 36, 14, 42, 15, 35, 27

Arrange the data in ascending order,

5, 14, 15, 17, 21, 22, 27, 33, 35, 36, 42

In that Data set,

15->lower quartile

22->median

35->upper quartile

Upper Quartile for Odd Data Set:

Let us see how to calculate the upper quartile of the data set that contains odd numbers.

Step 1: First find the median of the data set. The median divide the data set into upper and lower part.

Step 2: Find the median for upper part of the data set .That median is called as upper quartile.

Ex :   Find the upper quartile of the  data set  { 8, 49, 53, 19, 45, 44, 11, 41, 47, 51, 39}

Sol :  First we have to arrange the data set in order.

Ordered Data set:{ 8, 11, 19, 39, 41, 44, 45, 47,49,51,53}

Median (Mid value) =44

Lower part = { 8, 11, 19, 39, 41}

Upper part = { 45, 47,49,51,53 }

In the upper part of the data set,49 is the median.Having problem with how to write numbers in words keep reading my upcoming posts, i will try to help you.

So the Upper quartile (Median of upper part) of the data set is 49

Upper Quartile for even Data Set :

Let us see how to calculate the upper quartile of the data set that contains even numbers.

Step 1: Find the Median of the data set by calculating the average of the two middle number of the data set.

Step 2: Next in the upper part, find the median by calculating the average. That value is known as upper quartile.

Ex :  Find the upper quartile of the data set {13, 6, 24, 33, 9, 38, 16, 46, 19, 53, 26, 65}

Sol :   First we have to arrange the data set in order.

Ordered data set: { 6,9,13,16,19,24,26,33,38,46,53,65}

Total number of the data set is even, So

Median : (24+26)/2= 25

Upper part : {25,33,38,46,53,65}

Upper quartile :  (38+46)/2= 42