QUARTILE DEVIATION

OUTLINE OF THE PRESENTATION
 What is Coefficient of Variation?
 What are the Formulas of COV in
Excel
 How to find COV by Hand
 What is Quartile Deviation (Group
Data)
 How to calculate COV by Box and
Whisker Plot
 References

WHAT IS COEFFICIENT OF
VARIATION?
 The Coefficient of Variation (CV) also
known as Relative Standard Deviation
(RSD) is the ratio of the standard
deviation(σ) to the mean (μ).

Regular
Test
Randomized
Answers
Mean 59.9 44.8
SD 10.2 12.7
FOR EXAMPLE …
A RESEARCHER IS COMPARING TWO MULTIPLE CHOICE TEST WITH DIFFERENT CONDITIONS. IN
THE FIRST TEST, A TYPICAL MULTIPLE – CHOICE TEST IS ADMINISTERED. IN THE SECOND TEST,
ALTERNATIVE CHOICES ARE RANDOMLY ASSIGNED TO TEST TAKERS. THE RESULTS FROM THE
TWO TEST ARE:

HELPS TO MAKE SENSE OF DATA:
Regular
Test
Randomized
Answers
Mean 59.9 44.8
SD 10.2 12.7
CV 17.03 28.35

FORMULAS OF
COEFFICIENT
VARIATION
IN
EXCEL.XLSX

HOW TO FIND A
COEFFICIENT OF VARIATION
BY HAND
Step 1 : Divide the standard
Deviation by the mean for the
1st Sample:
11.2/50.1 = 0.22355
Step 2: Multiply step 1 by 100:
0.22355 * 100 = 22.355 %
Step 3: Divide the standard deviation
by the mean for the 2nd sample :
12.9/45.8 = 0.28166
Step 4: Multiply step 3 by 100:
0.28166 * 100 = 28.266 %
Regular
Test
Randomize
d Answers
Mean 50.1 45.8
SD 11.2 12.9

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.
Quartile Deviation Interquartile Range

EXAMPLE:
Calculate the
QD for a group of data
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

EXAMPLES:
 Min : 1
 Max: 10
 Median: 6
 Q1: 3
 Q3: 7
 IQR: 4
 Min: 2
 Max: 10
 Median: 5
 Q1: 2.5
 Q3: 7.5
 IQR: 5
{ 3, 7, 7, 3, 10, 1, 6, 6, 3 }
1, 3, 3, 6, 6, 7, 7, 10
{3, 10, 2, 8, 7, 5, 2, 5}
2, 2, 3, 5, 5, 7, 8, 10

REFERENCES:
 http://www.lexic.us/definition-of/quartile
 https://www.google.com.ph/search?q=QUARTILE+DEVIATION++FORMULA
&biw=1093&bih=471&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjqhanq
7IHSAhVEn5QKHW39BFcQ_AUIBigB#tbm=isch&q=box+and+whisky+plots
 http://www.purplemath.com/modules/boxwhisk.htm
 https://www.youtube.com/watch?v=FQqUmWPpI_M

“ALL THE STATISTICS
IN THE WORLD CAN'T
MEASURE THE
WARMTH OF A SMILE.”
― CHRIS HART

QUARTILE DEVIATION

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