Home » Ask & Discuss » Mathematics. » Algebra « Back to Discussion

Algebra

Hot goIITian

Joined:	18 Jan 2009
Post:	193

7 May 2009 01:26:55 IST

0 People liked this

342

STATISTICS Question

None

This is a question related to Statistics.

Does anyone know what QUARTILE DEVIATION is???

Please give the method explaining what it is and how to calculate it.

Last year, a question related to Quartile Deviation came in DCE-CEE.

Rates assured!!!

Share this article on:

Comments (4)

Ashwini

Moderator

Joined: 19 Aug 2008

Posts: 6831

8 May 2009 10:30:21 IST

Like 2 people liked this

The quartile deviation is also called semi-quartile range. It is defined as the amount of dispersion present in the middle of 50% of the values. The equation given by:

(Q₃ - Q₁)/2=Q_D

Where:
Q_D= the quartile deviation
Q₁= the first quartile
Q₃= the third quartile

"RAIDEN" :-)

Blazing goIITian

Joined: 17 Aug 2008

Posts: 451

8 May 2009 10:47:45 IST

Like 1 people liked this

Definitions

first quartile (designated Q₁) = lower quartile = cuts off lowest 25% of data = 25th percentile
second quartile (designated Q₂) = median = cuts data set in half = 50th percentile
third quartile (designated Q₃) = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile

The difference between the upper and lower quartiles is called the interquartile range.

Computing methods

There is no universal agreement on choosing the quartile values.

The formula for the position of the observation at a given percentile, y, with n data points sorted in ascending order is:

$L_y = (n+1)\left(\cfrac{y}{100}\right)$

Example

Example 4. Boxplot (with quartiles and an interquartile range) and a probability density function (pdf) of a normal N(0,1σ²) population

One possible rule (employed by the TI-83 calculator boxplot and 1-Var Stats functions) is as follows:

Use the median to divide the ordered data set into two halves. Do not include the median into the halves.
The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

The examples below assume this rule. Another possible rule would be to include the median in the halves when calculating the quartiles. This would give significantly different answers to the examples.

Example 1
Data Set: 6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36
Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

$\begin{cases}Q_1 = 15 \\Q_2 = 40 \\Q_3 = 43\end{cases}$

Example 2
Ordered Data Set: 7, 15, 36, 39, 40, 41

$\begin{cases}Q_1 = 15 \\Q_2 = 37.5 \\Q_3 = 40\end{cases}$

Example 3
Ordered Data Set: 1 2 3 4

$\begin{cases}Q_1 = 1.5 \\Q_2 = 2.5 \\Q_3 = 3.5\end{cases}$

XYZ

Hot goIITian

Joined: 18 Jan 2009

Posts: 193

8 May 2009 22:13:51 IST

Like 0 people liked this

Thanks a lot both of you!!! Really thankful to both of you for your kind help!!!

Thanks!!!

s faiyaz

Forum Expert

Joined: 30 Mar 2009

Posts: 335

8 May 2009 22:40:12 IST

Like 1 people liked this

The quartile deviation is half the difference between the upper and lower quartiles in a distribution. It is a measure of the spread through the middle half of a distribution. It can be useful because it is not influenced by extremely high or extremely low scores. Quartile Deviation is an ordinal statistic and is most often used in conjunction with the median.

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team