coefficient variation
Transcript of coefficient variation
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What is Coefficient of Variation?
What are the Formulas of COV in Excel
How to find COV by Hand Calculating Quartile
(Ungrouped Data) Calculating Quartile (Group Data) Calculating COV by Box and
Whisker Plot References
* Outline of the presentation
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The Coefficient of Variation (CV) also known as Relative Standard Deviation (RSD) is the ratio of the standard deviation(σ) to the mean (μ).
*What is Coefficient of Variation?
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Regular Test
Randomized Answers
Mean 59.9 44.8SD 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:
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* 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
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*Formulas of Coefficient Variation
in Excel.xlsx
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*How to find a Coefficient of
Variation by Hand
Regular Test
Randomized Answers
Mean 50.1 45.8
SD 11.2 12.9
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 %
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*Quartile Deviation
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Quartile Deviation Interquartile Range
* 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.
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Formulas:Keys:
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*Quartiles Raw or
Ungrouped Data
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25, 18, 30, 8, 15, 5,10, 35, 40, 455, 8, 10, 15, 18, 25, 30, 35, 40, 45
= () th Item= (2. 75) th Item= 2nd Item + () (3rd – 2nd )8 + 8 + x 2= 8+ 1.5= 9.5
*=3 x (2.75) th item*(8.25) th item*8th item + () [ 9th – 8th ]*= 35 + [ 40 – 35 ]*=35 + 1.25 *=36.25
Example:
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*Quartile Deviation
(Grouped
Data)
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EXAMPLE:
Calculate the QD for a group of data
Given Data…
241, 521, 421, 250, 300, 365, 840, 958.
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Click icon to add pictureSTEP 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
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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
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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
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*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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*Box and Whisker Plot
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{ 3, 7, 7, 3, 10, 1, 6, 6 }
1, 3 I 3, 6 I 6, 7 I 7, 10
*Min : 1*Max: 10*Median: 6
*Q1: 3*Q3: 7*IQR: 4
{ 3, 10, 2, 8, 7, 5, 2, 5 }
2, 2 I 3, 5 I 5, 7 I 8, 10
*Min: 2*Max: 10*Median: 5
*Q1: 2.5*Q3: 7.5*IQR: 5
*Example:
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*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
*https://www.youtube.com/watch?v=ybHABoAlIQE
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* “All the statistics in the world can't measure
the warmth of a smile.”
― Chris Hart
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