The . . . . . . . . of the Chi-squared distribution is twice the degrees of freedom.

variance
standard deviation
mode
none of the mentioned

The correct answer is: variance.

The variance of a chi-squared distribution is twice the degrees of freedom. This is because the chi-squared distribution is a scaled version of the gamma distribution, and the variance of a gamma distribution is equal to its degrees of freedom multiplied by its scale parameter.

The variance of a random variable is a measure of how spread out its values are. A low variance indicates that the values are clustered close to the mean, while a high variance indicates that the values are spread out over a wider range.

The degrees of freedom of a chi-squared distribution are the number of independent pieces of information that are used to calculate the chi-squared statistic. For example, if you have a sample of 10 data points and you are calculating the chi-squared statistic for a goodness-of-fit test, then the degrees of freedom would be 9.

The mode of a distribution is the value that occurs most often in the distribution. The mode of a chi-squared distribution is not defined, because there is no value that occurs more often than any other.

In conclusion, the variance of a chi-squared distribution is twice the degrees of freedom. This is because the chi-squared distribution is a scaled version of the gamma distribution, and the variance of a gamma distribution is equal to its degrees of freedom multiplied by its scale parameter.