Question

If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation?

Short answer

When the number of degrees of freedom for a chi-square distribution is $25,$the population mean is $25$ and the standard deviation is$7.07.$

Step-by-step solution

Given information

Given in the question that, We need to find the population mean and standard deviation if the number of degrees of freedom for a chi-square distribution is$25$.

Explanation

The population mean in a chi-square distribution is given as

${\mu }_{x^2}=df$

and the standard deviation is calculated as

${\sigma }_{x^2}=\sqrt{2\times df}$

The degree of freedom is now set to$25$in the question, and the population mean is determined as follows:

${\mu }_{x^2}=df$

$=25$

$\Rightarrow {\mu }_{x^2}=25$

Also known as standard deviation, it is determined as follows:

${\sigma }_{x^2}=\sqrt{2\times df}$

$$\begin{gathered} =\sqrt{2\times 25} \\ =\sqrt{50} \\ =7.071 \\ \approx 7.07 \end{gathered}$$

$\Rightarrow {\sigma }_{x^2}=7.07$