The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below :Subject Mathematics Physics Chemistry Biology Mean Marks 40 28 38 36 SD 15 12 14 16
What is the coefficient of variation of marks in Mathematics ?
37.5%
Calculating Coefficient of Variation for Mathematics Marks
The coefficient of variation (CV) is a statistical measure used to assess the relative variability of data. It expresses the standard deviation as a percentage of the mean, allowing for the comparison of variability between data sets with different scales or means. A lower coefficient of variation indicates less dispersion relative to the mean.
The formula for calculating the coefficient of variation (CV) is given by:
\(\text{CV} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100\%\)
From the provided data about the marks obtained by 50 students in 4 subjects, we can extract the required values for Mathematics.
| Subject | Mean Marks | SD |
|---|---|---|
| Mathematics | 40 | 15 |
| Physics | 28 | 12 |
| Chemistry | 38 | 14 |
| Biology | 36 | 16 |
For Mathematics marks:
- Mean (\(\bar{x}\)) = 40
- Standard Deviation (\(\sigma\)) = 15
Now, we can calculate the coefficient of variation for Mathematics by substituting these values into the formula:
\(\text{CV}_{\text{Mathematics}} = \left( \frac{\sigma_{\text{Mathematics}}}{\bar{x}_{\text{Mathematics}}} \right) \times 100\%\)
\(\text{CV}_{\text{Mathematics}} = \left( \frac{15}{40} \right) \times 100\%\)
First, calculate the ratio of standard deviation to the mean:
\(\frac{15}{40} = 0.375\)
Now, multiply the result by 100% to express it as a percentage:
\(\text{CV}_{\text{Mathematics}} = 0.375 \times 100\% = 37.5\%\)
Thus, the coefficient of variation for marks in Mathematics is 37.5%.
Comparing this calculated value with the given options, we find that 37.5% matches Option 1.
The coefficient of variation helps understand the variability in Mathematics marks relative to the average performance in that subject.
Revision Table: Key Statistical Concepts
| Term | Description | Formula/Symbol |
|---|---|---|
| Mean | The average of a set of numbers. | \(\bar{x}\) |
| Standard Deviation (SD) | A measure of the amount of variation or dispersion of a set of values. | \(\sigma\) |
| Coefficient of Variation (CV) | A relative measure of variability, expressed as a percentage of the mean. Useful for comparing dispersion between different datasets. | \(\left( \frac{\sigma}{\bar{x}} \right) \times 100\%\) |
Additional Information on Coefficient of Variation
The coefficient of variation is particularly useful when comparing the variability of two or more datasets that have different units of measurement or significantly different means. For instance, comparing the variability of heights (measured in cm) and weights (measured in kg) within a group, or comparing the variability of marks in two subjects where the average marks are very different. A lower CV indicates that the data points are relatively closer to the mean, suggesting lower relative variability or greater consistency within that dataset compared to another dataset with a higher CV.
Similar Questions
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Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?
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