A. M = 60, S = 14
B. M = 70, S = 16
C. M = 80, S = 5
D. M = 90, S = 4
Choose the correct answer from the options given below:
Calculating Coefficient of Variation for Datasets
This question requires us to calculate the Coefficient of Variation (CV) for four different datasets (A, B, C, and D) and then arrange them in ascending order based on their CV values. The Coefficient of Variation is a useful statistical measure that indicates the extent of variability in relation to the mean.
Understanding Coefficient of Variation (CV)
The Coefficient of Variation (CV) is defined as the ratio of the standard deviation (S) to the mean (M). It is often expressed as a percentage. The formula is:
$$ CV = \frac{S}{M} \times 100\% $$
A lower CV indicates less variability relative to the mean, while a higher CV indicates more variability.
Computing CV for Each Dataset
We will calculate the CV for each dataset using the provided Mean (M) and Standard Deviation (S).
| Dataset | Mean (M) | Standard Deviation (S) | Calculation ($ \frac{S}{M} \times 100\% $) | Coefficient of Variation (CV) |
|---|---|---|---|---|
| A | 60 | 14 | $ \frac{14}{60} \times 100\% $ | $ \approx 23.33\% $ |
| B | 70 | 16 | $ \frac{16}{70} \times 100\% $ | $ \approx 22.86\% $ |
| C | 80 | 5 | $ \frac{5}{80} \times 100\% $ | $ \approx 6.25\% $ |
| D | 90 | 4 | $ \frac{4}{90} \times 100\% $ | $ \approx 4.44\% $ |
Arranging Datasets in Ascending Order
Now, we arrange the datasets based on their calculated Coefficient of Variation values from smallest to largest:
- Dataset D: $ \approx 4.44\% $
- Dataset C: $ \approx 6.25\% $
- Dataset B: $ \approx 22.86\% $
- Dataset A: $ \approx 23.33\% $
Therefore, the datasets arranged in ascending order of their Coefficient of Variation are D, C, B, A.
Final Answer Selection
Comparing this order with the given options, the correct option is the one that lists the datasets as D, C, B, A.
Important Questions from Measures of Dispersion
When Mean deviation is divided by the average used in finding out the mean deviation itself, the resulting quantity is described as_____________.
.Match List - I with List - II.
List - I List - II (A) Coefficient of Dispersion (I) Standard deviation as a percentage of mean (B) Standard Deviation (II) Mean of squared deviations of individual scores from mean (C) Coefficient of variation (III) Variance in terms of mean (D) Variance (IV) Positive square root of variance - Two sets of data consisting of 10 and 20 observations have same mean 8 with standard deviations of 1 and 2, respectively. If the two data sets are combined, then the variance is
Two data set of sizes 9 and 6 have standard deviation 3 and 4 respectively and arithmetic means 3 respectively. The standard deviation of combined data set of size 15 is
Variance is independent of change of :
