Marks obtained by 7 students in a subject are 30,55,75,50,50,60,39. The number of students securing marks less than the mean marks is
(a)7
(b)6
(c)5
(d)4

Options

A. 7
B. 6
C. 5
D. 4

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the sum of the marks obtained by the students.
The marks obtained by the students are: 30, 55, 75, 50, 50, 60, and 39.

\[ \text{Sum} = 30 + 55 + 75 + 50 + 50 + 60 + 39 \]

Calculating the sum:

\[ 30 + 55 = 85 \]
\[ 85 + 75 = 160 \]
\[ 160 + 50 = 210 \]
\[ 210 + 50 = 260 \]
\[ 260 + 60 = 320 \]
\[ 320 + 39 = 359 \]

So, the total sum of the marks is **359**.

### Step 2: Calculate the mean (average) of the marks.
The mean is calculated using the formula:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

In this case, the number of observations (students) is 7.

\[ \text{Mean} = \frac{359}{7} \]

Calculating the mean:

\[ 359 \div 7 = 51.2857 \approx 51.29 \text{ (rounded to two decimal places)} \]

So, the mean marks are approximately **51.29**.

### Step 3: Determine how many students scored less than the mean.
Now, we will compare each student's marks with the mean (51.29):

- Student 1: 30 (less than 51.29)
- Student 2: 55 (not less than 51.29)
- Student 3: 75 (not less than 51.29)
- Student 4: 50 (less than 51.29)
- Student 5: 50 (less than 51.29)
- Student 6: 60 (not less than 51.29)
- Student 7: 39 (less than 51.29)

Counting the number of students who scored less than the mean:

- Students who scored less than the mean: 30, 50, 50, 39 (Total: 4 students)

### Conclusion
The number of students securing marks less than the mean marks is **4**.

Thus, the answer is **(d) 4**.

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