Question

Emmett gathered some data to compare the monthly cost of renting a one-bedroom apartment in Dallas and Austin. The data collected for the monthly cost of renting a one-bedroom apartment in Dallas is shown below.
$994 $1,322 $1,075 $1,189 $1,172
$1,465 $1,215 $930 $1,090 $1,288
The data collected for the monthly cost of renting a one-bedroom apartment in Austin is shown below.

$1,450 $1,400 $1,375 $1,389 $1,296
$900 $1,250 $1,100 $950 $1,495

Select ALL the statements that are true about the Austin Data.
This city's data had the higher interquartile range of the two cities by $87.
This city's data had the higher median monthly apartment cost of the two cities by $155.
this city's data had the lower average apartment cost because the mean was $86.50 less than that of the other set of data.
This city's data had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data.

Answer 1

Answer:

The correct options are;

a) The city's data has the higher median monthly apartment cost of the two cities by $155

b) The city's data had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data

Step-by-step explanation:

The given data for the cost of renting a one-bedroom apartment in Dallas is presented as follows;

$994, $1,322, $1,075, $1,189, $1,172, $1,465, $1,215, $930, $1,090, $1,288

Which can be arranged in increasing order and analyzed to find the interquartile range, mean and standard deviation using Microsoft Excel as follows;

$930, $994, $1,075, $1,090, $1,172, $1,189, $1,215, $1,288, $1,322, and $ 1,465

The first quartile, Q₁ = $1,054.75

The third quartile, Q₃ = $1,296.5

The interquartile range = Q₃ - Q₁ = $241.75

The median = $1,180.5

The average monthly cost = $1,174

The standard deviation of the sample = $159.9597

The given data for the cost of renting a one-bedroom apartment in Austin is presented in increasing order using Microsoft Excel as follows;

$900, $950, $1,100, $1,250, $1,296, $1,375, $1,389, $1,400, $1,450, $1,495

The interquartile range, mean and standard deviation are found using Microsoft Excel as follows;

The first quartile, Q₁ = $1,062.5

The third quartile, Q₃ = $1,412.5

The interquartile range = Q₃ - Q₁ = $1,412.5 - $1,062.5 = $350

The median = $1,335.5

The average monthly cost = $1,260.5

The standard deviation of the sample = $209.0945

The difference in the median cost of the two cities is $1,335.5 - $1,180.5 = $155

Therefore, the Austin's city data has the higher median monthly apartment cost of the two cities by $155

b) The difference in the sample standard deviation of the two cities is $209.0945 - $159.9597 = $49.13476

Therefore, the Austin city data had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data.

Answer 2

Answer:

This city's data had the higher median monthly apartment cost of the two cities by $155.

This city's data had the higher interquartile range of the two cities by $87.

This city's data had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data.

Step-by-step explanation:

Austin Mean: 1335.5

Dallas Mean: 1180.5

Interquartile Range (Austin): 300

Interquartile Range (Dallas): 213

Standard Deviation (Austin): 209.0945

Standard Deviation (Dallas): 159.9597