Calculate the Mean Deviation from the mean of the following data: Bonus 10 15 20 25 30 : : : : : : : : : : : Frequency 5 4 4 4 3

Step 1: Compute the Mean ($\bar{X}$)

The mean is calculated using the formula: $$\bar{X}=\frac{\sum f\cdot X}{\sum f}$$ From the table: $$\sum f=5+4+4+4+3=20$$ $$\sum f\cdot X=50+60+80+100+90=380$$ Thus, $$\bar{X}=\frac{380}{20}=19$$

Step 2: Compute Absolute Deviations from the Mean

Calculate $|X-\bar{X}|$ for each value of $X$:

Step 3: Compute Weighted Absolute Deviations

Multiply each $|X-\bar{X}|$ by its corresponding frequency ($f$):

Sum of weighted absolute deviations: $$\sum f\cdot |X-\bar{X}|=45+16+4+24+33=122$$

Step 4: Compute Mean Deviation

The mean deviation from the mean is given by: $$\text{Mean Deviation}=\frac{\sum f\cdot |X-\bar{X}|}{\sum f}$$ Substituting the values: $$\text{Mean Deviation}=\frac{122}{20}=6.1$$

Final Answer: The mean deviation from the mean is 6.1.