Question

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

Explanation:

Step1: Find the range

The range is calculated by subtracting the minimum value from the maximum value.
For the set \(42,10,36,51,70,28\), the minimum value \(= 10\) and the maximum value \(= 70\).
So, the range \(=70 - 10=60\).

Step2: Find the mid - range

The mid - range is calculated by \(\frac{\text{Minimum}+\text{Maximum}}{2}\).
Substituting the values, mid - range \(=\frac{10 + 70}{2}=\frac{80}{2}=40\).

Now let's check each option:

• Option 1: The range is \(60\) and mid - range is \(30\). Since mid - range \(=40

eq30\), this option is wrong.

• Option 2: The range is \(14\) and mid - range is \(35\). Since range \(=60

eq14\), this option is wrong.

• Option 3: The range is \(70\) and mid - range is \(39\). Since range \(=60

eq70\) and mid - range \(=40
eq39\), this option is wrong.

• Option 4: The range is \(60\) (calculated as \(70 - 10\)) and mid - range \(=40\). Since \(60>40\), the range is larger than the mid - range.

Answer:

The range is larger than the midrange.