Marks obtained by four students are : 25, 35, 45, 55.
The average deriations from the mean is

Options

A. 10
B. 9
C. 7
D. none of these

Answer

To find the average deviation from the mean for the marks obtained by four students (25, 35, 45, 55), we will follow these steps:

### Step 1: Calculate the Mean
The mean (average) is calculated by summing all the values and dividing by the number of values.

\[ \text{Mean} (x̄) = \frac{25 + 35 + 45 + 55}{4} \]

Calculating the sum:

\[ 25 + 35 + 45 + 55 = 160 \]

Now, divide by the number of students (4):

\[ x̄ = \frac{160}{4} = 40 \]

### Step 2: Calculate the Deviations from the Mean
Next, we calculate the absolute deviations of each mark from the mean:

1. For 25:
\[ |25 - 40| = | -15 | = 15 \]

2. For 35:
\[ |35 - 40| = | -5 | = 5 \]

3. For 45:
\[ |45 - 40| = |5| = 5 \]

4. For 55:
\[ |55 - 40| = |15| = 15 \]

### Step 3: Sum the Absolute Deviations
Now, sum all the absolute deviations calculated in the previous step:

\[ \text{Total Absolute Deviations} = 15 + 5 + 5 + 15 = 40 \]

### Step 4: Calculate the Average Deviation
Finally, we calculate the average deviation by dividing the total absolute deviations by the number of values (n):

\[ \text{Average Deviation} = \frac{\text{Total Absolute Deviations}}{n} = \frac{40}{4} = 10 \]

### Final Answer
The average deviation from the mean is **10**.

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