coefficient variation

statistics

1. 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

2. The Coefficient of Variation (CV ) also known as R elative Standard Deviation (RSD) is the ratio of the s tandard deviation (σ) to the mean (μ) . What is Coefficient of Variation?

3. 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:

4. 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

5. Formulas of Coefficient Variation in Excel.xlsx

6. 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 1 st 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 2 nd sample : 12.9/45.8 = 0.28166 Step 4: Multiply step 3 by 100: 0.28166 * 100 = 28.266 %

7. Quartile Deviation

8. 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.

9. Formulas: Keys:

10. Quartiles Raw or Ungrouped Data

11. 25, 18, 30, 8, 15, 5,10, 35, 40, 45 5, 8, 10, 15, 18, 25, 30, 35, 40, 45 = ( ) th Item = (2. 75) th Item = 2 nd Item + ( ) (3 rd – 2 nd ) 8 + 8 + x 2 = 8+ 1.5 = 9.5   =3 x (2.75) th item (8.25) th item 8 th item + ( ) [ 9 th – 8 th ] = 35 + [ 40 – 35 ] =35 + 1.25 =36.25   Example:

12. Quartile Deviation (Grouped Data)

13. EXAMPLE: Calculate the QD for a group of data Given Data… 241, 521, 421, 250, 300, 365, 840, 958.

14. 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

15. 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

16. 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

17. Step 7: Now, find the median value between Q3 and Q1 . Quartile Deviation = Q3-Q1/2 = 680.5 - 275/2 = 202.75

18. Box and Whisker Plot

19. { 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 :

20. 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

21. “All the statistics in the world can't measure the warmth of a smile .”   ―  Chris Hart

22. ROSELYN 