Question

1. the table below gives the temperature in degrees fahrenheit for 5 rivers last monday.

if the median of the 5 temperatures was 68°f, which of the following could have
been the temperature in river c last friday?

river
temperature
(degrees fahrenheit)
a
68°f
b
52°f
c
x°f
d
73°f
e
76°f

Explanation:

Step1: Recall the concept of median

For a set of \(n = 5\) (odd - numbered) data points \(a_1,a_2,a_3,a_4,a_5\) sorted in ascending order, the median is \(a_3\).

Step2: Sort the known values

Sort the known temperatures: \(52^{\circ}F,68^{\circ}F,73^{\circ}F,76^{\circ}F\).
Let's consider the possible positions of \(x\) (temperature of River C) for the median to be \(68^{\circ}F\).
Case 1: If \(x\leq68\), when we sort the data \(x,52,68,73,76\) (if \(x\leq52\)) or \(52,x,68,73,76\) (if \(52 < x\leq68\)), the median is \(68\).
Case 2: If \(x\geq68\), when we sort the data \(52,68,x,73,76\) (if \(68\leq x\leq73\)) or \(52,68,73,x,76\) (if \(73 < x\leq76\)) or \(52,68,73,76,x\) (if \(x > 76\)), the median is \(68\).

Answer:

Any value \(x\) such that \(x\) is a real number (since temperature is a real - valued quantity) and there is no upper or lower bound restriction other than the nature of temperature (in a practical sense, but mathematically) \(x\in R\) (but if we assume the data is in a reasonable range for river temperatures, and considering the median condition). If we assume the options (not shown in the problem statement but based on the median formula), values like \(x = 68\) (when we consider the non - strict inequality for the median position). But if we just go by the median formula for \(n = 5\) data points \(y_1,y_2,y_3,y_4,y_5\) (sorted) with median \(y_3\), and our known values \(52,68,73,76\), \(x\) can be any value such that when sorted, the third - value is \(68\). So \(x\leq73\) (because if \(x > 73\), when we sort \(52,68,73,x,76\) (if \(x\leq76\)) or \(52,68,73,76,x\) (if \(x>76\)), the median is still \(68\)). A common value that satisfies the condition (if we assume a multiple - choice context where one of the options fits the range) could be \(68^{\circ}F\) (for example, if \(x = 68\), the sorted data is \(52,68,68,73,76\) and the median is \(68\)).