The mean of a distribution is 24 and the standard deviation is 6. What is the value of variance coefficient? A. 50% B. 25% C. 100% D. 75%
B
Understanding the Coefficient of Variation Calculation
The question asks for the "variance coefficient," which is more commonly known as the coefficient of variation (CV). The coefficient of variation is a measure of the relative variability of data with respect to the mean. It is useful for comparing the degree of variation between data sets, even if their means are drastically different. It is expressed as a percentage.
Formula for Coefficient of Variation
The formula to calculate the coefficient of variation (CV) is:
Applying the Given Data
We are given the following values:
- Mean ($\bar{x}$) = 24
- Standard Deviation ($\sigma$) = 6
Now, we can substitute these values into the formula:
Thus, the value of the coefficient of variation is 25%.
Final Answer Determination
Based on our calculation, the coefficient of variation is 25%. This matches option B.
Revision Table: Key Statistical Measures
| Measure | Description | Formula (Sample) |
|---|---|---|
| Mean | Average value | $$ \bar{x} = \frac{\sum x_i}{n} $$ |
| Standard Deviation | Measure of spread from the mean | $$ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} $$ |
| Variance | Square of standard deviation | $$ s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1} $$ |
| Coefficient of Variation | Relative measure of variability | $$ CV = \left( \frac{s}{\bar{x}} \right) \times 100\% $$ |
Additional Information: Understanding Coefficient of Variation
The coefficient of variation is a dimensionless quantity, meaning it does not have any units. This makes it particularly useful for comparing distributions that are measured in different units or have significantly different means. A lower CV indicates less dispersion relative to the mean, while a higher CV indicates more dispersion relative to the mean. It is often used in fields like finance (comparing volatility of different assets), engineering, and physical sciences.
It's important to note that the coefficient of variation is only meaningful when the mean is a non-zero value. If the mean is zero or very close to zero, the CV can become infinite or unstable, and alternative measures of variability should be used.
Important Questions from Standard Deviation
Calculate the mean from the following table.
Scores
Frequencies
0-10
2
10-20
4
20-30
12
30-40
21
40-50
6
50-60
3
60-70
2
Find the standard deviation of the following data (rounded off to two decimal places).
5, 3, 4, 7
If the standard deviation of a population is 5, what will be its variance?
A. 10
B. 15
C. 25
D. 12.5
The variance of a set of data is 196. Then the standard deviation of the data is.
A. ± 14
B. 14
C. 96
D. 98The variance of a set of data is 144. Then the standard deviation of the data is:
A. ±12
B. 12
C. 44
D. 72
