The _________ is the arithmetic mean of the squared deviation from the mean.Question 8Answera.estimatorb.madiatorc.varianced.predictor

The correct answer is c. variance.

Explanation

The variance is a statistical term that represents the degree of spread or dispersion of a set of values. It quantifies how much the values in a dataset deviate from the arithmetic mean (average) of the dataset. Specifically, to calculate the variance, one computes the differences between each value and the mean, squares those differences, and then takes the average of those squared deviations. This process prevents negative differences from canceling out positive differences, giving a clear sense of the overall variability in the data.

In more formal terms, if $x_1, x_2, \ldots, x_n$ are the data points, and $\mu$ is the mean of these data points, the variance $\sigma^2$ is calculated as:

$\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2$

Where:

• $n$ is the number of data points,
• $x_i$ represents each data point,
• $\mu$ is the mean of the data points.

Understanding variance is crucial in statistics as it lays the groundwork for many other statistical concepts, including standard deviation and analysis of variance (ANOVA).