What is the mean of the integers from $25$ to $41$ inclusive?

• A. $30$
• B. $34$
• C. $33$
• D. $32$

Answer: (C)

Verified step by step guidance

1. Identify the range of integers given, which are from 25 to 41 inclusive.
2. Calculate the number of integers in this range using the formula: \(\text{number of terms} = 41 - 25 + 1\).
3. Find the sum of the integers from 25 to 41. Since these are consecutive integers, use the formula for the sum of an arithmetic series: \(\text{sum} = \frac{\text{number of terms}}{2} \times (\text{first term} + \text{last term})\).
4. Calculate the mean by dividing the sum by the number of terms: \(\text{mean} = \frac{\text{sum}}{\text{number of terms}}\).
5. Interpret the result as the average value of all integers from 25 to 41 inclusive.