Final answer:
The portion of the variance calculation, [∑ (x-µ)2], is called the sum of squared deviations.
Explanation:
The sum of squared deviations is a crucial component in the calculation of variance, which is a measure of how spread out a set of data is from its mean. In this portion of the calculation, each data point (x) is subtracted from the mean (µ) and then squared. This process is repeated for all the data points, and the resulting values are then summed together. The sum of squared deviations is a way to quantify the total amount of variation within a data set.
To better understand this concept, let's look at an example. Suppose we have a data set with the following values: 2, 4, 6, 8, and 10. The mean of this data set is 6. To calculate the sum of squared deviations, we first subtract the mean from each data point. This gives us the following values: -4, -2, 0, 2, and 4. Next, we square each of these values, resulting in 16, 4, 0, 4, and 16. Finally, we add these values together, which gives us a sum of 40. This is the sum of squared deviations for our data set.
The sum of squared deviations is important because it represents the total amount of variation in a data set. The larger the sum of squared deviations, the more spread out the data is from the mean. In the example above, we can see that the data set has a relatively large sum of squared deviations, indicating that there is a significant amount of variation within the data.
Additionally, the sum of squared deviations is used to calculate the variance of a data set. In fact, it is the first step in the calculation of variance. Once we have the sum of squared deviations, we divide it by the number of data points to get the average squared deviation. This value is then used to calculate the variance by taking the square root of the average squared deviation.
In conclusion, the portion of the variance calculation [∑ (x-µ)2] is known as the sum of squared deviations. It is a fundamental part of the calculation of variance and provides a measure of the total amount of variation within a data set. By understanding the concept of sum of squared deviations, we can better understand how variance is calculated and how it is used to analyze and interpret data.