Official Explanation
The Table provides detailed data about specific apartments, including information about rent, square footage, and certain amenities. The text accompanying the table also provides average values for the three numeric columns in the table. Jot these down.
Avg rent: $1,428
Avg size: 692 sf
Avg rate ($ / sf): $2.09
Statement 1: No. The language in this Probability statement is tricky. The first part (units with some kind of a parking option) defines the sub-group from which you’ll be working: only those units with a parking option. Sort by Parking option to see which units apply.
6 units have some kind of parking option: Units A and D have covered parking, units G and I have garage parking, and units E and J have lot parking. Next, of these 6 units, how many exceed both the average monthly rent and the average rate?
The average monthly rent is $1,428 and the average rate is $2.09. Glance down the Monthly rent column for just the first 6 units (still sorted by Parking option). The first 4 (A, D, G, and I) all exceed the monthly rent; the final 2 (E and J) do not, so ignore them.
Of the 4 that exceed the monthly rent (A, D, G, and I), which ones also exceed the average rate of $2.09? Three do: A, G, and I.
Of the 6 units with a parking option, 3 exceed both the average rent and the average rate, so the chance is 3/6, or 50%, which is higher than 30%, not lower. This statement is not true.
Statement 2: No. This statement tests a Statistics concept: the median. Think about what you need to do before you start calculating. The rent is determined by multiplying the rate ($ per square foot) for the unit by the size (square feet) of that unit. The size of apartment H does not change—only the rate changes. If H’s rate is higher than the median rate, then changing to the median rate will result in a rent decrease. If, on the other hand, H’s rate is lower than the median rate, then changing to the median rate will result in a rent increase. Your task, then, is to find H’s rate and compare it to the median rate.
Unit H’s rate is $2.01.
To find the median rate, sort by the Rate column. There are 12 units total, so the units in 5th and 6th position (units H and C) are the two middle units. Take the average of their rates to find the median rate for the whole list.
\(\frac{2.01 + 2.12}{2}=2.065\)
The median rate is higher than H’s current rate, so switching to the median rate would result in a rent increase for this unit, not a decrease. The statement is not true.
Statement 3: Yes. This statement tests another Statistics topic. A positive correlation between two things means that, as one gets larger or more likely to occur, the other also gets larger or more likely to occur. So, as the rate increases, does the likelihood of having covered or garage parking also increase? Sort by Rate ($ per sqft). Note that three of the four units with the highest rates per square foot also have either covered or garage parking. In addition, only one of the apartments with lower rates per square foot has either covered or garage parking. This indicates a positive correlation.
Answer: No, No and Yes