Question

Which of the statements below is true for the following set of numbers?20, 15, 50, 85, 75, 60a) The range is 85 and the midrange is 55.b) The range is 70 and the midrange is 35.c) The range and the midrange are equal.d) The range is 70 and the midrange is 50.

Answer 1

RANGE

The range of a given data is the difference between the largest and smallest numbers.

Steps for solving range:

Step 1: Arrange the data values in ascending order

$\Rightarrow15,20,50,60,75,85$

Step 2: Identify the largest and smallest numbers

$\begin{gathered} Largest=85 \\ Smallest=15 \end{gathered}$

Step 3: Calculate the difference between the numbers.

$\begin{gathered} Range=Largest-Smallest \\ \therefore \\ Range=85-15=70 \end{gathered}$

The range is 70.

MIDRANGE

The midrange of a given set of data is the average of the largest and smallest number.

Steps for solving midrange:

Step 1: Arrange the data values in ascending order

$\Rightarrow15,20,50,60,75,85$

Step 2: Identify the largest and smallest numbers

$\begin{gathered} Largest=85 \\ Smallest=15 \end{gathered}$

Step 3: Calculate the average of the numbers.

$\begin{gathered} Midrange=\frac{Largest-Smallest}{2} \\ \therefore \\ Midrange=\frac{85-15}{2} \\ Midrange=\frac{70}{2} \\ Midrange=35 \end{gathered}$

The midrange is 35.

ANSWER:

The correct option is OPTION B.