The standard deviation `(sigma)` of variate x is the square root of the A.M. of the squares of all deviations of x from the A.M. observations.
If `x_i//f_i`, i=1,2,… n is a frequency distribution then `sigma=sqrt(1/N Sigma_(i=1)^(n) f_i(x_i-barx)^2), N=Sigma_(i=1)^(n) f_i` and variance is the square of standard deviation. Coefficient of dispersion is `sigma/x` and coefficient of variation is `sigma/x xx 100`
For a given distribution of marks mean is 35.16 and its standard deviation is 19.76 then coefficient of variation is

Options

A. (a)1.778
B. (b)0.562
C. (c)177.8
D. (d)56.2

Answer

To find the coefficient of variation for the given distribution of marks, we will follow these steps:

### Step 1: Understand the given data
We are given:
- Mean (x̄) = 35.16
- Standard Deviation (σ) = 19.76

### Step 2: Use the formula for Coefficient of Variation
The formula for the coefficient of variation (CV) is given by:
\[ CV = \left( \frac{\sigma}{x̄} \right) \times 100 \]

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ CV = \left( \frac{19.76}{35.16} \right) \times 100 \]

### Step 4: Calculate the fraction
Now, we will calculate the fraction:
\[ \frac{19.76}{35.16} \approx 0.561 \]

### Step 5: Multiply by 100 to get the percentage
Now, we multiply by 100 to convert it into a percentage:
\[ CV \approx 0.561 \times 100 \approx 56.1 \]

### Step 6: Conclusion
Thus, the coefficient of variation is approximately 56.1%.

### Final Answer:
The coefficient of variation is **56.1%**.

---