Study done on a group of patients showed coefficient of variance for BP and serum creatinine to be 20%& 15% respectively. Inference is that -
Coefficient of variance

Coefficient of variance indicates how large standard deviation is relative to mean, i.e. Coefficient of variance is a relative comparison of a standard deviation to its mean. It is expressed as percentage.

CV = Standard deviation / mean x 100


For example, if the standard deviation of a sample is 8 and the sample mean is 44. The CV will be 18.2% . That means the standard deviation is 18.2% of the value of mean.

Significance of coefficient of variance

CV is a measure used to Compare relative variability when the mean is different in sample to be compared or in character (variables) to be compared —


CV compares variability of two different characteristics (e.g., BP, Serum creatinine, height, weight etc.) in the same group of subjects. In this situation mean BP of the sample will have different value (e.g., 120) and mean creatinine level will have different value (e.g., 0.8) in the same group (sample).
CV can compare variability of the same character in two or more different groups (samples). For example taking the height in a group from India and in other group from USA. Both the samples will have different mean height.


In these situations, when the mean is different for characteristics to be compared, CV is used to compare the relative variability.
Taking the example of given question :
CV for BP in a group is 20%.
CV for serum creatinine in the same group is 15%.
That means for BP, standard deviation is 20% of the mean; and for creatinine, standard deviation is 15% of the mean.
It has already been explained that standard deviation is measure of variation (deviation). Therefore, in the given question variability is more in BP than in serum creatinine value.
So, Coefficient of variance is used to compare variability of two different characteristic in same group or to compare variability of the same character in different groups (as the mean is different in both these situations).
Since coefficient of variance is a ratio, it has no units of measurement (dimensionless). It can be used to compare variability irrespective of the units of measurement used in two or more different group.
For example
It can compare variability if height measures as cm in one group & inches in another group.

About option 'c & d'


We cannot comment on standard deviation by knowing just only the coefficient of variance because we don’t know the mean BP and mean creatinine level of the sample group → In three related variables (Here CV, SD & mean) you must know the value of two variables to comment on value of the third one.
However, in this question we can say that the standard deviation relative to mean is large for BP than for serum creatinine.
So, we cannot comment on absolute value of standard deviation (whether SD of BP is more or SD of creatinine is more), But we can comment on standard deviation relative to mean.
Variation in BP is more than in serum creatinine
Variation in serum creatinine is more than in BP
Standard deviation of BP is more than of creatinine
Standard deviation of creatinine is more than of BP