The mean deviation about the mean for the data

is equal to :

To calculate the Mean Deviation about the Mean for the given frequency distribution, we follow a systematic process involving finding the arithmetic mean first, followed by the absolute deviations.

The mean for grouped data is given by the formula:

$$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$

Let's calculate the components:

$$\bar{x} = \frac{234}{26} = 9$$

The formula for Mean Deviation is:

$$M.D.(\bar{x}) = \frac{\sum f_i |x_i - \bar{x}|}{\sum f_i}$$

Now, let's find the absolute deviations $$|x_i - 9|$$ and their products with frequencies:

| $$x_i$$ | $$f_i$$ | $$|x_i - 9|$$ | $$f_i |x_i - 9|$$ |

| :--- | :--- | :--- | :--- |

| 5 | 8 | $$|5 - 9| = 4$$ | $$8 \times 4 = 32$$ |

| 7 | 6 | $$|7 - 9| = 2$$ | $$6 \times 2 = 12$$ |

| 9 | 2 | $$|9 - 9| = 0$$ | $$2 \times 0 = 0$$ |

| 10 | 2 | $$|10 - 9| = 1$$ | $$2 \times 1 = 2$$ |

| 12 | 2 | $$|12 - 9| = 3$$ | $$2 \times 3 = 6$$ |

| 15 | 6 | $$|15 - 9| = 6$$ | $$6 \times 6 = 36$$ |

| Total | 26 | | 88 |

Substitute the sums into the formula:

$$M.D.(\bar{x}) = \frac{88}{26}$$

Simplifying the fraction by dividing both numerator and denominator by 2:

$$M.D.(\bar{x}) = \frac{44}{13}$$

Final Answer: C ($$\frac{44}{13}$$)