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For a frequency distribution mean deviat...

For a frequency distribution mean deviation from mean in computed by `MdotDdot=(sumf)/(sumf|d|)` (b) `MdotDdot=(sumd)/(sumf)` (c) `MdotDdot=(sumfd)/(sumf)` (d) `MdotDdot=(sumf|d|)/(sumf)`

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To solve the question regarding the formula for calculating the mean deviation from the mean in a frequency distribution, we will follow these steps: ### Step-by-Step Solution: 1. **Understand the Definitions**: - Let \( x_i \) be the values of the data points. - Let \( f_i \) be the frequency of each data point \( x_i \). - The mean of the distribution, denoted as \( \bar{x} \), is calculated using the formula: \[ \bar{x} = \frac{\sum f_i x_i}{\sum f_i} \] 2. **Calculate the Deviations**: - The deviation of each data point from the mean is given by \( d_i = x_i - \bar{x} \). - The absolute deviation is \( |d_i| = |x_i - \bar{x}| \). 3. **Calculate the Weighted Absolute Deviations**: - For each data point, multiply the absolute deviation by its frequency: \[ f_i |d_i| = f_i |x_i - \bar{x}| \] 4. **Sum the Weighted Absolute Deviations**: - The total weighted absolute deviation is given by: \[ \sum f_i |d_i| = \sum f_i |x_i - \bar{x}| \] 5. **Calculate the Mean Deviation**: - The mean deviation from the mean is calculated using the formula: \[ M_d = \frac{\sum f_i |d_i|}{\sum f_i} \] - This formula represents the mean of the absolute deviations weighted by their frequencies. 6. **Identify the Correct Option**: - From the options provided, we can see that: - (d) \( M_d = \frac{\sum f_i |d|}{\sum f_i} \) - This matches our derived formula for mean deviation. ### Conclusion: The correct formula for the mean deviation from the mean in a frequency distribution is: \[ M_d = \frac{\sum f_i |d|}{\sum f_i} \] Thus, the answer is option (d).

To solve the question regarding the formula for calculating the mean deviation from the mean in a frequency distribution, we will follow these steps: ### Step-by-Step Solution: 1. **Understand the Definitions**: - Let \( x_i \) be the values of the data points. - Let \( f_i \) be the frequency of each data point \( x_i \). - The mean of the distribution, denoted as \( \bar{x} \), is calculated using the formula: ...
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For a frequency distribution standard deviation is computed by applying the formula\ sigma=sqrt((sumfd^2)/(sumf)-((sumfd^)/(sumf))^2) (b) sigma=sqrt(((sumfd^2)/(sumf))-(sumfd^2^)/(sumf)) (c) sigma=sqrt((sumfd^2)/(sumf)-(sumfd^^)/(sumf)) (d) sqrt(((sumfd^)/(sumf))^2-(sumfd^2^)/(sumf))

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