If there are n observations with 23 and 57 as their smallest and largest observations respectively then the value of mid-range is ____________.

1. Break Down the Problem

To find the mid-range, we need to calculate the average of the smallest and largest observations.

2. Relevant Concepts

The formula to calculate Mid-Range is given by: $\text{Mid-Range} = \frac{\text{Smallest Observation} + \text{Largest Observation}}{2}$

3. Analysis and Detail

Given:

• Smallest Observation (S) = 23
• Largest Observation (L) = 57

Using the formula: $\text{Mid-Range} = \frac{23 + 57}{2}$

4. Verify and Summarize

Calculating the mid-range: $\text{Mid-Range} = \frac{80}{2} = 40$ The calculations confirm that the mid-range value is correct.

Final Answer

The mid-range is $\boxed{40}$.