There are two different formulas or methods that can be used to calculate SS.
under what circumstances is the definitional formula easy to use?
When n is small?
The definitional formula for calculating SS (Sum of Squares) is typically easier to use when the dataset is small or has simple values. It involves manually calculating the deviation of each data point from the mean, squaring those deviations, and summing them up. This formula is given by:
SS_definitional = Σ(xi - μ)^2
where xi represents each individual data point, μ is the mean of the dataset, and Σ denotes summation.
To calculate SS using the definitional formula, follow these steps:
1. Calculate the mean (μ) of the dataset by summing up all the values and dividing by the total number of data points.
2. Subtract the mean (μ) from each individual data point (xi) to find the deviation from the mean.
3. Square each deviation obtained in step 2.
4. Sum up all the squared deviations calculated in step 3 to get the Sum of Squares (SS_definitional).
The definitional formula can be useful when working with small datasets or when you want to understand the calculations involved in finding the SS by hand. However, for larger datasets or complex values, it can be time-consuming and prone to manual errors. In such cases, using alternative methods like the computational formula or statistical software might be more convenient and accurate.