Forty-nine cities provided information on vacancy rates (in percent) for local apartments in the following frequency distribution. Vacancy Rate (in percent) Frequency 0 up to 3 6 3 up to 6 6 6 up to 9 11 9 up to 12 21 12 up to 15 5 a. Calculate the average vacancy rate. b. Calculate the variance and the standard deviation for this sample. Variance: Standard deviation:

Step-by-step explanation:

For this case we can calculate all the questions with the following table:

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

____________________________________

0-3          1.5                6        9           13.5

3-6          4.5               6        27          121.5

6-9          7.5               11        82.5      618.75

9-12         10.5             21       220.5    2315.25

12-25       18.5             5        18           1711.25

_____________________________________

Total                           49      431.5        4780.25

We can calculate the expected value with the following formula:

And if we replace we got:

We can calculate the sample variance with the following formula:

And replacing we got:

And the deviation would be just the square root of the variance like this:

right

step-by-step explanation:

it shoild be o

step-by-step explanation: