Question

For a frequency distribution, the mean deviation about the mean is computed by

• A. M.D = \( \frac{\Sigma d_i}{\Sigma f_i} \)
• B. M.D = \( \frac{\Sigma f_i d_i}{\Sigma f_i} \)
• C. M.D = \( \frac{\Sigma f_i |d_i|}{\Sigma f_i} \)
• D. M.D = \( \frac{\Sigma f_i |d_i|}{\Sigma f_i} \)

Hint:

To calculate the mean deviation, always use the absolute value of the deviations and divide the weighted sum by the total frequency.

Answer 1

The Correct Option is C

We are tasked with finding the formula for the mean deviation (M.D.) of a frequency distribution about the mean.
Step 1: Understand the formula for M.D.
The formula for the mean deviation about the mean is: \[ M.D = \frac{\Sigma f_i |d_i|}{\Sigma f_i} \] where:
\( f_i \) is the frequency of the \( i \)-th observation,
\( d_i \) is the deviation of the \( i \)-th observation from the mean,
\( |d_i| \) is the absolute value of the deviation.

Step 2: Conclusion
Thus, the correct formula for the mean deviation about the mean is \( M.D = \frac{\Sigma f_i |d_i|}{\Sigma f_i} \), corresponding to option (c).