The following relative frequency distribution was constructed from a population of 400. Calculate the population mean, the population variance, and the population standard deviation. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Class Relative Frequency −20 up to −10 0.22 0.22 −10 up to 0 0.340.32 0 up to 10 0.380.34 10 up to 20 0.06

For the variance first we need to find the second moment given by:

And if we replace we got:

And then the variance is given by:

And the deviation is given by:

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.  

Solution to the problem

Let X our random variable of interest.

For this case we can calculate the mean , variance and deviation creating the following table:

Class          Midpoint(xi)    fi           xi*fi     xi^2 *fi

-20 to-10         -15           0.22        -3.3      49.5

-10-0                 -5           0.34        -1.7        8.5

0-10                   5           0.38         1.9        9.5

10-20                15           0.06        0.9       13.5

And for this case we can find the expected value with the following formula:

And if we replace we got:

For the variance first we need to find the second moment given by:

And if we replace we got:

And then the variance is given by:

And the deviation is given by:

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column