Question

In: Statistics and Probability

Fifty cities provided information on vacancy rates (in percent) for local apartments in the following frequency...

Fifty 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	5
3 up to 6	5
6 up to 9	10
9 up to 12	20
12 up to 15	10

a. Calculate the average vacancy rate.

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.)

Expert Solution

Solution:

Given that

Class	Frequency	Mid value	fx	fx²
0 - 3	5	1.5	7.5	11.25
3 - 6	5	4.5	22.5	101.25
6 - 9	10	7.5	75	562.5
9 - 12	20	10.5	210	2205
12 - 15	10	13.5	135	1822.5
	n = 50		fx = 450	fx² = 4702.5

Solution:

Given that

a ) The sample mean is

Mean = (fx/ n)

= (450 / 50 )

= 9

The average vacancy rate = 9

b ) The sample variance S²

S² = (fx² ) - (( fx )² / n ) / 1 -n ) * h²

= ( 4702.5 ( ( 450 )² / 50 ) / 49

= ( 4702.5 - 4050 / 50 ) / 49

= 652.5 / 49

= 13.3163

The sample variance S² is 13.32

The standard deviation = sample variance

= 13.3163

= 3.6492

The standard deviation = 3.65

orchestra answered 2 years ago

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