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.
