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

Randomized

Answers

Mean 50.1 45.

8

SD 11.2 12.9

QUARTILE DEVIATIO

N(GROUP DATA)

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

Formulas: Keys:

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

BOX AND WHISKER PLOT

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=0ahUKEwjqhanq7IHSAhVEn5QKHW39BFcQ_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

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