If in a series which is not highly skewed the mean deviation is `7*8`, the approximate value of its standard deviation is

Options

A. `9*75`
B. `8*37`
C. `10*2`
D. none of these

Answer

To find the approximate value of the standard deviation given that the mean deviation is 7.8 in a moderately skewed distribution, we can follow these steps:

### Step 1: Understand the relationship between Mean Deviation and Standard Deviation
For a moderately skewed distribution, the relationship between the mean deviation (MD) and the standard deviation (SD) is given by the formula:
\[ MD = \frac{4}{5} \times SD \]

### Step 2: Rearrange the formula to find Standard Deviation
We can rearrange the formula to express the standard deviation in terms of the mean deviation:
\[ SD = \frac{5}{4} \times MD \]

### Step 3: Substitute the value of Mean Deviation
Now, we substitute the given value of mean deviation (MD = 7.8) into the equation:
\[ SD = \frac{5}{4} \times 7.8 \]

### Step 4: Calculate the Standard Deviation
Now, we perform the multiplication:
\[ SD = \frac{5 \times 7.8}{4} = \frac{39}{4} = 9.75 \]

### Step 5: Final Calculation
To express it in decimal form:
\[ SD = 9.75 \]

Thus, the approximate value of the standard deviation is **9.75**.