4. 4
COEFFICIENT OF VARIANCE
The coefficient of variation (CV) is the ratio of the standard deviation to the mean (average). For
example, the expression “The standard deviation is 15% of the mean” is a CV. The CV is
particularly useful when you want to compare results from two different surveys or tests that
have different measures or values.
FORMULA
Coefficient of Variation = (Standard Deviation / Mean) * 100.
5. 5
Methodology
Ø To obtain the first objective that is comparison of marks of high school, intermediate and
graduation:
• Select data analysis → descriptive statistic → select input range (marks of all three years)→
select labels in first row and summary statistics →select ok
• By following the above procedure we get the statistical summary for marks of all three years.
Ø To obtain the second objective that is cat percentile on the basis of gender first the data was
sorted on gender basis then following procedure was followed:
• Select data analysis → descriptive statistic → select input range (male percentile)→ select labels
in first row and summary statistics →select ok
Ø To get statistical summary for females instead of selecting male marks female marks were
selected.
• Select data analysis → descriptive statistic → select input range (female percentile)→ select
labels in first row and summary statistics →select ok
Ø To obtain third objective that is cat percentile on the basis of subject history first the data
was sorted on the basis of subject history then following procedure was followed:
• Select data analysis → descriptive statistic → select input range (cat percentile of students with
professional background)→ select labels in first row and summary statistics →select ok
• Same thing was followed for science, commerce and art and humanities students and a
comparative data was gained.
• Coefficient of variation was calculated on the basis of high school, intermediate and graduation
marks.
• On the basis of subject history and gender, coefficient of variance was also calculated
6. 6
INTERPRETATION
Table 1 : Comparison Of High School, Intermediate, Graduation Marks
High School Intermediate Graduation
Mean 69.60967742 Mean 71.27419355 Mean 64.27419355
Standard Error 1.158688033 Standard Error 1.126848761 Standard Error 0.679910933
Median 69.5 Median 72 Median 63
Mode 60 Mode 78 Mode 63
Standard Deviation 9.123518693
Standard
Deviation 8.872816018
Standard
Deviation 5.353624036
Sample Variance 83.23859334 Sample Variance 78.72686409 Sample Variance 28.66129032
Kurtosis -0.96008286 Kurtosis -0.545786638 Kurtosis -0.514794602
Skewness 0.173562885 Skewness -0.044635766 Skewness 0.493438425
Range 37 Range 38 Range 23
Minimum 52 Minimum 51 Minimum 54
Maximum 89 Maximum 89 Maximum 77
Sum 4315.8 Sum 4419 Sum 3985
Count 62 Count 62 Count 62
Analysis:-
High School
Ø High school marks mean is 69.9, while median is 69.5. So we can say that there is no outlier
present in the data.
Ø Skewness of High School students is 0.17. Hence we can say that the data is equally
distributed.
Ø Coefficient of variance is 13.1 (approx) for High School.
Intermediate
Ø Intermediate marks mean is 71.2, while median is 72. So we can say that there is no outlier
present in the data.
Ø Skewness of Intermediate is -0.04. Hence we can say that the data is negatively skewed i.e.,
it is inclined towards left.
Ø Coefficient of variance is 12.4 (approx) for Intermediate.
Graduation
Ø Graduation marks mean is 64.2, while median is 63. So we can say that there is no outlier
present in the data.
Ø Skewness of Graduation marks is 0.49. Hence we can say that data is equally distributed.
Ø Coefficient of variance is 8.3 (approx) for Graduation.
Ø According to coefficient of variance Graduation data is most consistent while data of High
School is most inconsistent.
7. 7
Table 2: Comparison Of Cat Percentile On The Basis Of Subject History
Professional Science Commerce
Arts And
Humanities
Mean 71.5 Mean 69.125 Mean 71.5714286 Mean 66.666667
Standard Error 3.12976909 Standard Error 3.35891227 Standard Error 1.83976403 Standard Error 2.0275875
Median 72 Median 68.5 Median 70 Median 67
Mode 83 Mode 55 Mode 75 Mode #N/A
Standard
Deviation 10.8418382
Standard
Deviation 13.4356491
Standard
Deviation 9.73511617
Standard
Deviation 3.5118846
Sample Variance 117.545455 Sample Variance 180.516667 Sample Variance 94.7724868 Sample Variance 12.333333
Kurtosis -0.9638502 Kurtosis
-
1.34678967 Kurtosis
-
0.13457186 Kurtosis #DIV/0!
Skewness
-
0.44401337 Skewness 0.22544531 Skewness 0.63567894 Skewness
-
0.4232732
Range 31 Range 40 Range 37 Range 7
Minimum 54 Minimum 50 Minimum 55 Minimum 63
Maximum 85 Maximum 90 Maximum 92 Maximum 70
Sum 858 Sum 1106 Sum 2004 Sum 200
Count 12 Count 16 Count 28 Count 3
Analysis:-
Professional
Ø Professional data mean is 71.5, while median is 72. So we can say that there are outliers
present in the data
Ø Skewness of the data is 0.44. Hence we can say that the data is equally distributed.
Ø Coefficient of variance is 15.1 (approx) for professional background students.
Science
Ø Science data mean is 69.1, while median is 68.5. So we can say that there are no outliers
present in the data.
Ø Skewness of the data is 0.22. Hence we can say that the data is equally distributed.
Ø Coefficient of variance is 19.3 (approx) for science background students.
Commerce
Ø Commerce data mean is 71.5, while median is 70. So we can say that there are no outliers
present in the data.
Ø Skewness of the data is 0.63. Hence we can say that the data is equally distributed.
Ø Coefficient of variance is 13.5 (approx) for commerce background students.
Arts And Humanities
Ø Arts and Humanities data mean is 66.6, while median is 67. So we can say that there are no
outliers present in the data.
Ø Skewness of the data is 0.42. Hence we can say that the data is equally distributed.
Ø Coefficient of variance is 5.2 (approx) for Arts and Humanities students.
Ø According to coefficient of variance most consistent data is of Arts and Humanities followed
by Commerce, Professional and Science being the most inconsistent.
