The mean marks obtained by seven in a group is 226 . If the marks obtained by six of them are 340, 180 , 260 , 56 , 275 and 307 respectively , find the marks obtained by the seventh student.

Options

A. 164
B. 226
C. 340
D. cannot be determined

Answer

To find the marks obtained by the seventh student, we can follow these steps:

### Step 1: Understand the Mean
The mean (average) is calculated by dividing the sum of all observations by the total number of observations. In this case, we know the mean marks of seven students is 226.

### Step 2: Calculate the Total Marks for Seven Students
Since the mean is 226 and there are 7 students, we can find the total marks obtained by all seven students using the formula:
\[ \text{Total Marks} = \text{Mean} \times \text{Number of Students} \]
Substituting the values:
\[ \text{Total Marks} = 226 \times 7 \]
Calculating this gives:
\[ \text{Total Marks} = 1582 \]

### Step 3: Calculate the Total Marks of the Six Students
Now, we need to find the total marks obtained by the six students whose marks are given:
- Marks of the six students: 340, 180, 260, 56, 275, and 307.

Calculating the sum of these marks:
\[ \text{Total Marks of Six Students} = 340 + 180 + 260 + 56 + 275 + 307 \]
Calculating this step-by-step:
- \(340 + 180 = 520\)
- \(520 + 260 = 780\)
- \(780 + 56 = 836\)
- \(836 + 275 = 1111\)
- \(1111 + 307 = 1418\)

Thus, the total marks of the six students is:
\[ \text{Total Marks of Six Students} = 1418 \]

### Step 4: Find the Marks of the Seventh Student
Now, we can find the marks obtained by the seventh student by subtracting the total marks of the six students from the total marks of all seven students:
\[ \text{Marks of Seventh Student} = \text{Total Marks} - \text{Total Marks of Six Students} \]
Substituting the values:
\[ \text{Marks of Seventh Student} = 1582 - 1418 \]
Calculating this gives:
\[ \text{Marks of Seventh Student} = 164 \]

### Final Answer
The marks obtained by the seventh student is **164**.

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