IBM Data Science Practice Test

Why is the mean important in calculating variance and standard deviation?

1. It accounts for all data values in the dataset

2. It serves as a stabilizer against outliers

3. It represents the average, which is essential for these calculations

4. It outlines the frequency of datasets

The correct answer is: It represents the average, which is essential for these calculations

The mean is crucial in calculating variance and standard deviation because it serves as the reference point or central value around which the data is distributed. When calculating variance, you first find the difference between each data point and the mean, square these differences to eliminate negative values, and then average those squared differences. This process directly ties the mean to the calculations, as it determines how far each data point is from the average. Standard deviation, which is derived from variance, also uses the mean in the same manner. It provides an insight into the spread or dispersion of the dataset in relation to the mean. By focusing on how data points differ from the mean mathematically, both variance and standard deviation effectively quantify the variability within the dataset. Thus, the average is essential for these calculations, making the choice that emphasizes its importance the best option.