Final answer:
To compute Σxᵢ² * fᵢ, we rearrange the variance formula and insert the given values, resulting in Σxᵢ² * fᵢ = 10300.
Step-by-step explanation:
The student is asking to compute Σxᵢ² * fᵢ given S² = 10, Σxᵢ * fᵢ = 300, and Σfᵢ = 30. This problem involves finding the sum of the squares of the x values times their frequencies, which is a typical calculation in statistics when finding the variance or standard deviation.
To find Σxᵢ² * fᵢ, we use the formula for the variance S², which in this context looks like:
S² = (Σxᵢ² * fᵢ) / Σfᵢ - (Σxᵢ * fᵢ / Σfᵢ)²
Rearranging the formula to solve for Σxᵢ² * fᵢ gives us:
Σxᵢ² * fᵢ = S² * Σfᵢ + (Σxᵢ * fᵢ)² / Σfᵢ
Plugging in the given values, we find:
- Σxᵢ² * fᵢ = 10 * 30 + (300)² / 30
- Σxᵢ² * fᵢ = 300 + 10000
- Σxᵢ² * fᵢ = 10300
Therefore, based on the given conditions, Σxᵢ² * fᵢ equals 10300.