Question

hirty-five 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 7 3 up to 6 5 6 up to 9 6 9 up to 12 8 12 up to 15 9 a. Calculate the average vacancy rate. (Round your answer to 4 decimal places.) b. Calculate the variance and the standard deviation for this sample. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Answer 1

Given: n - total number of cities = 35

Vacancy rate and their corresponding frequencies are given.

The formula to find the average rate and sample variance is,

Where f - frequency and x - the midpoint of the class interval.

The formula to find the midpoint is

The table for calculation is,

Vacancy rate	x	Frequency f	fx	(x-mean)2	(x-mean)2 f
0-3	1.5	7	10.5	43.56	304.92
3-6	4.5	5	22.5	12.96	64.8
6-9	7.5	6	45	0.36	2.16
9-12	10.5	8	84	5.76	46.08
12-15	13.5	9	121.5	29.16	262.44
Total		35	283.5		680.4

a) Average vacancy rate.

b) Sample variance

Sample variance = 20.01

Standard deviation is the square root of the variance

Therefore, Variance = 20.01 and Standard deviation = 4.47