Learn How to Calculate the Quartile Deviation for Group Data - Tutorial

How to Calculate the Quartile Deviation for Group Data - Definition and Example

Definition:

Quartile Deviation (QD) means the semi variation between the upper quartiles (Q3) and lower quartiles (Q1) in a distribution. Q3 - Q1 is referred as the interquartile range.

Formula:

QD = Q3 - Q1/ 2
Example:

Calculate the QD for a group of data, 241,521,421,250,300,365,840,958.

Solution:

Given data = { 241,521,421,250,300,365,840,958 }

Step 1:

First, arrange the given digits in ascending order = 241,250,300,365,421,521,840,958. Total number of given data (n) = 8.

Step 2:

Calculate the center value (n/2) for the given data {241,250,300,365,421,521,840,958}. n=8
n/2 = 8/2
n/2 = 4. From the given data, { 241,250,300,365,421,521,840,958 } the fourth value is 365

Step 3:

Now, find out the n/2+1 value. i.e n/2 +1 = 4+1=5 From the given data, { 241,250,300,365,421,521,840,958 } the fifth value is 421

Step 4:

From the given group of data, { 241,250,300,365,421,521,840,958 } Consider, First four values Q1 = 241,250,300,365 Last four values Q3 = 421,521,840,958

Step 5:

Now, let us find the median value for Q1. Q1= {241,250,300,365} For Q1, total count (n) = 4 Q1(n/2) = Q1(4/2) = Q1(2) i.e) Second value in Q1 is 250 Q1( (n/2)+1 ) = Q1( (4/2)+1 ) = Q1(2+1) = Q1(3) i.e) Third value in Q1 is 300 Median (Q1) = ( Q1(n/2) + Q1((n/2)+1) ) / 2 (Q1) = 250+300/2 (Q1) = 550/2 = 275

Step 6:

Let us now calculate the median value for Q3. Q3= {421,521,840,958} For Q3, total count (n) = 4 Q3(n/2) = Q3(4/2) = Q3(2) i.e) Second value in Q3 is 521 Q3( (n/2)+1 ) = Q3( (4/2)+1 ) = Q3(2+1) = Q3(3) i.e) Third value in Q3 is 840. Median (Q3) = ( Q1(n/2) + Q1((n/2)+1) ) / 2 (Q3) = ( 521 + 840 ) / 2 (Q3) = 1361/2 = 680.5

Step 7:

Now, find the median value between Q3 and Q1. Quartile Deviation = Q3-Q1/2 = 680.5 - 275/2 = 202.75

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