# He following table shows the probability distribution for a discrete random variable. What is the variance of X?

## X 11 14 16 19 21 23 24 29 P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08 The mean of the discrete random variable X is 18.59.

May 17, 2018

$\text{variance} = 23.182$

#### Explanation:

The variance of X is equal to the standard deviation of X squared:

"variance" = ("standard deviation")^2

Refer to this link on mathisfun.com for details on calculating variance manually.

I used my TI-84+.

• Enter the data into two lists. Press "stat", then "enter" in order to edit the lists
• I used ${L}_{1}$ for $X$ and ${L}_{2}$ for $P \left(X\right)$.
• Next, press "stat", move right to "calc", then "enter" in order to calculate 1-variable statistics on X.
• Confirm that ${L}_{2}$ is the frequency list for ${L}_{1}$, and press "calculate".
• The screen should show the standard deviation ${\sigma}_{x} = 4.8148$

Finally, square the standard deviation to get
$\textcolor{b l u e}{\text{variance} = 23.1819}$