Question

the table above gives the high temperature in degrees fahrenheit for 5 cities last friday. if the median of the 5 temperatures was 31° f, which of the following could have been the high temperature in city c last friday. 32° f 30°f 45°f 60°f

Explanation:

Step1: Recall Median Definition

The median of 5 (odd number) values is the 3rd value when sorted in ascending order.

Step2: List Known Temperatures

Known temperatures: \(15^\circ\text{F}\) (City B), \(31^\circ\text{F}\) (City A), \(47^\circ\text{F}\) (City D), \(53^\circ\text{F}\) (unknown city, say E). Let City C's temp be \(x\).

Step3: Sort and Analyze Median

When sorted, the 3rd value must be \(31^\circ\text{F}\). So, after sorting, the order should have at least two values \(\leq 31\) and two values \(\geq 31\).

• For \(x = 32^\circ\text{F}\): Sorted list: \(15, 31, 32, 47, 53\). Median is \(32\) (not 31, invalid).
• For \(x = 30^\circ\text{F}\): Sorted list: \(15, 30, 31, 47, 53\). Median is \(31\) (valid).
• For \(x = 45^\circ\text{F}\): Sorted list: \(15, 31, 45, 47, 53\). Median is \(45\) (not 31, invalid).
• For \(x = 60^\circ\text{F}\): Sorted list: \(15, 31, 47, 53, 60\). Median is \(47\) (not 31, invalid).

Answer:

30°F (the option with 30°F, e.g., if options are labeled as: the second option (30°F) in the list)