The variance is the mean squared deviation of all the values from the mean.Select one:TrueFalse

Answer

The statement "The variance is the mean squared deviation of all the values from the mean" is True.

Explanation

Variance is a statistical measure that describes the dispersion of a set of data points around their mean. It quantifies how much the values in a data set deviate from the average value. The calculation involves the following steps:

1. Calculate the Mean: Determine the average of the data set.
2. Deviate Each Value from the Mean: Subtract the mean from each data point to find the deviation.
3. Square Each Deviation: Square each of the deviations obtained in the previous step.
4. Calculate the Mean of Squared Deviations: Take the average of these squared deviations to determine the variance.

Mathematically, if $X = \{x_1, x_2, \ldots, x_n\}$ is a data set and $\mu$ is the mean of $X$, the variance $Var(X)$ is given by:

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

This confirms that the variance is indeed the mean of the squared deviations from the mean.