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Find the mean deviation from the mean o...

Find the mean deviation from the mean of the following discrete data 6,7, 10,1213,4,12 ,16

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To find the mean deviation from the mean of the given discrete data: 6, 7, 10, 12, 13, 4, and 16, we will follow these steps: ### Step 1: Calculate the Mean The mean (average) of the data set is calculated using the formula: \[ \text{Mean} ( \bar{x} ) = \frac{\sum x_i}{n} \] Where \( x_i \) are the data points and \( n \) is the number of data points. Given data: 6, 7, 10, 12, 13, 4, 16 Calculating the sum: \[ \sum x_i = 6 + 7 + 10 + 12 + 13 + 4 + 16 = 68 \] The number of data points \( n = 7 \). Now, substituting into the mean formula: \[ \bar{x} = \frac{68}{7} \approx 9.71 \] ### Step 2: Calculate the Absolute Deviations Next, we find the absolute deviations from the mean for each data point: \[ |x_i - \bar{x}| \] Calculating each deviation: - For 6: \( |6 - 9.71| \approx 3.71 \) - For 7: \( |7 - 9.71| \approx 2.71 \) - For 10: \( |10 - 9.71| \approx 0.29 \) - For 12: \( |12 - 9.71| \approx 2.29 \) - For 13: \( |13 - 9.71| \approx 3.29 \) - For 4: \( |4 - 9.71| \approx 5.71 \) - For 16: \( |16 - 9.71| \approx 6.29 \) ### Step 3: Sum of Absolute Deviations Now, we sum these absolute deviations: \[ \text{Sum of absolute deviations} = 3.71 + 2.71 + 0.29 + 2.29 + 3.29 + 5.71 + 6.29 = 24.29 \] ### Step 4: Calculate the Mean Deviation Finally, we calculate the mean deviation using the formula: \[ \text{Mean Deviation} = \frac{\sum |x_i - \bar{x}|}{n} \] Substituting the values: \[ \text{Mean Deviation} = \frac{24.29}{7} \approx 3.47 \] ### Final Answer The mean deviation from the mean of the given data is approximately **3.47**. ---
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