Median weight of 100 children was 12 kgs. The Standard Detion was 3.Calculate the percentage coefficient of variance –
**Core Concept**
The coefficient of variation (CV) is a statistical measure used to express the relative variability of a dataset. It is calculated as the ratio of the standard deviation (SD) to the mean, multiplied by 100 to express it as a percentage. In this context, the CV is used to describe the spread of weights among the children.
**Why the Correct Answer is Right**
To calculate the CV, we divide the SD (3 kg) by the mean (12 kg), and then multiply by 100. This gives us (3 / 12) x 100 = 25%. The CV is a useful measure of variability, as it allows us to compare the spread of different datasets. In this case, a CV of 25% indicates that the weights of the children are relatively consistent, with a small amount of variation.
**Why Each Wrong Option is Incorrect**
**Option B:** 35% is incorrect because it is greater than the calculated CV, suggesting more variability in the weights than actually exists.
**Option C:** 45% is incorrect for the same reason as Option B. It overestimates the variability in the weights.
**Option D:** 55% is incorrect because it is even more extreme than Options B and C. It would suggest a large amount of variability in the weights, which is not supported by the data.
**Clinical Pearl / High-Yield Fact**
When working with datasets that have a small number of observations (like this one), it's essential to be cautious when interpreting measures of variability. A small sample size can lead to artificially high or low values for measures like the CV.
**Correct Answer:**
✓ Correct Answer: A. 25%