Finding a missing mark from the group mean: The mean marks of a group of 7 students is 226. If six marks are 340, 180, 260, 56, 275, and 307, what is the seventh student’s mark?

Introduction / Context:
Given a group mean and all but one values, we can compute the missing value from totals. This is a direct application of the definition of mean.

Given Data / Assumptions:

• n = 7 students; mean = 226
• Known six marks: 340, 180, 260, 56, 275, 307

Concept / Approach:
Total = n * mean. Subtract the sum of known marks from the total to get the missing mark.

Step-by-Step Solution:
Total = 7 * 226 = 1582Sum of known six = 340 + 180 + 260 + 56 + 275 + 307 = 1418Seventh mark = 1582 − 1418 = 164

Verification / Alternative check:
Plugging 164 back, the seven marks sum to 1582, and 1582 / 7 = 226 exactly.

Why Other Options Are Wrong:
226 and 340 are existing or distractor numbers; “cannot be determined” is false because totals suffice; 188 does not satisfy the mean requirement.

Common Pitfalls:
Arithmetic slips when adding multiple numbers—group them carefully to avoid mistakes.

Final Answer:
164