Question

find the variance for the given data round your answer to one more decimal place in the original data the normal monthly precipitation in inches for August is listed for 12 different US cities 3.5, 1.6, 2.4, 3.7, 4.1, 3.9, 1.0, 3.6, 4.2, 3.4, 3.7, 2.2.

Answer 1

Answer:

The variance of given data is approximately 1.09

Step-by-step explanation:

We are given the following data:

3.5, 1.6, 2.4, 3.7, 4.1, 3.9, 1.0, 3.6, 4.2, 3.4, 3.7, 2.2

Formula:

$\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{37.3}{12} =3.108$

Sum of squares of differences = 12.029

$\sigma^2 =\dfrac{12.029}{11} = 1.0024 \approx 1.09$

Thus, the variance of given data is approximately 1.09