Question

table below shows the high temperatures last thursday for five cities, a through e. city high temperature a $t^{circ}f$ b $87^{circ}f$ c $81^{circ}f$ d $62^{circ}f$ e $93^{circ}f$ the median of the thursday high temperature for these cities was $81^{circ}f$, which of the following could not have been the high temperature last thursday for city a? 55°f 75°f 85°f 65°f clear all

Explanation:

Step1: Recall median concept

For 5 data - points, the median is the 3rd value when the data is arranged in ascending or descending order.

Step2: Arrange known temperatures

The known temperatures in ascending order are \(62^{\circ}F\), \(81^{\circ}F\), \(87^{\circ}F\), \(93^{\circ}F\).

Step3: Analyze possible values of \(t\)

Since the median is \(81^{\circ}F\), when we arrange all 5 temperatures in order, \(t\) must be such that \(81^{\circ}F\) is the middle - value. So \(t\leq81^{\circ}F\).

Answer:

C. \(85^{\circ}F\)