Final answer:
The coefficient of variation for the dataset with a sum of 500, the sum of squares of 6000, and a median of 12, is approximately 44.7%.
Step-by-step explanation:
The student has provided information regarding a set of 50 observations, including the sum of the observations (500), the sum of their squares (6000), and the median value (12). We need to calculate the coefficient of variation, which measures the extent of variability in relation to the mean of the data.
To calculate the coefficient of variation, we need to compute the mean (μ) and the standard deviation (SD). The mean is the sum of the observations divided by the number of observations.
Mean (μ) = Sum of observations / Number of observations = 500 / 50 = 10
Next, we compute the variance using the formula:
Variance (σ²) = (Sum of squares / Number of observations) - (Mean²)
Variance = (6000 / 50) - (10²) = 120 - 100 = 20
Then, the standard deviation (SD) is the square root of the variance:
Standard Deviation (SD) = √(Variance) = √(20)
Now, the coefficient of variation (CV) is calculated as:
Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100%
Coefficient of Variation (CV) = (√(20) / 10) × 100% = (4.47 / 10) × 100% ≈ 44.7%
The coefficient of variation is approximately 44.7%, which measures the extent of variability in relation to the average of the data.