Question

which of the statements below is true for the following set of numbers?
42, 10, 36, 51, 70, 28
the range is 14 and the midrange is 35.
the range is 60 and the midrange is 30.
the range is 70 and the midrange is 39.
the range is larger than the midrange.

Explanation:

Step1: Find the maximum and minimum values

First, identify the maximum and minimum numbers in the set {42, 10, 36, 51, 70, 28}. The maximum value (max) is 70, and the minimum value (min) is 10.

Step2: Calculate the range

The range is calculated as \( \text{range} = \max - \min \). So, \( \text{range} = 70 - 10 = 60 \).

Step3: Calculate the midrange

The midrange is calculated as \( \text{midrange} = \frac{\max + \min}{2} \). So, \( \text{midrange} = \frac{70 + 10}{2} = \frac{80}{2} = 40 \)? Wait, no, wait. Wait, let's re - check. Wait, maybe I made a mistake. Wait, the set is 42, 10, 36, 51, 70, 28. Max is 70, min is 10. Then midrange is (70 + 10)/2 = 40? But the options: Let's check the options again. Wait, maybe I miscalculated. Wait, no, let's check each option:

First, calculate range: 70 - 10 = 60.

Midrange: (70 + 10)/2 = 40? But the options have "The range is larger than the midrange". Let's check: range is 60, midrange is 40. 60>40, so "The range is larger than the midrange" is true.

Wait, let's check other options:

Option 1: range 14, midrange 35. 70 - 10 is 60≠14. So wrong.

Option 2: range 60, midrange 30. (70 + 10)/2 = 40≠30. Wrong.

Option 3: range 70, midrange 39. 70 - 10 = 60≠70. Wrong.

Option 4: range is 60, midrange is 40. 60>40, so "The range is larger than the midrange" is true.

Answer:

The range is larger than the midrange.