Question

which of the statements below is true for the following set of numbers? 20, 15, 50, 85, 75, 60 the range is 85 and the midrange is 55. the range and the midrange are equal. the range is 70 and the midrange is 35. the range is 70 and the midrange is 50.

Explanation:

Step1: Find the range

First, identify the maximum and minimum values in the set \(20, 15, 50, 85, 75, 60\). The minimum value (\(min\)) is \(15\) and the maximum value (\(max\)) is \(85\). The range is calculated as \(max - min\), so \(85 - 15 = 70\).

Step2: Find the midrange

The midrange is calculated as \(\frac{max + min}{2}\). Substituting the values of \(max = 85\) and \(min = 15\), we get \(\frac{85 + 15}{2}=\frac{100}{2}=50\).

Step3: Analyze the options

• Option 1: Range is \(85\) (incorrect, we found range is \(70\)) and midrange \(55\) (incorrect, midrange is \(50\)).
• Option 2: Check if range (\(70\)) and midrange (\(50\)) are equal. No, they are not.
• Option 3: Range is \(70\) (correct) but midrange \(35\) (incorrect, midrange is \(50\)).
• Option 4: Range is \(70\) (correct) and midrange is \(50\) (correct).

Answer:

The range is 70 and the midrange is 50. (The option stating "The range is 70 and the midrange is 50.")