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Find the mean deviation of first 7 natur...

Find the mean deviation of first 7 natural numbers from their mean.

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To find the mean deviation of the first 7 natural numbers from their mean, we can follow these steps: ### Step 1: Identify the first 7 natural numbers. The first 7 natural numbers are: 1, 2, 3, 4, 5, 6, 7. ### Step 2: Calculate the mean of these numbers. The mean (μ) is calculated using the formula: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \] Calculating the sum: \[ 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 \] Now, divide by the number of values (which is 7): \[ \text{Mean} = \frac{28}{7} = 4 \] ### Step 3: Calculate the absolute deviations from the mean. Now, we need to find the absolute deviations of each number from the mean (4): - |1 - 4| = 3 - |2 - 4| = 2 - |3 - 4| = 1 - |4 - 4| = 0 - |5 - 4| = 1 - |6 - 4| = 2 - |7 - 4| = 3 ### Step 4: Calculate the mean of these absolute deviations. Now, we will sum the absolute deviations: \[ 3 + 2 + 1 + 0 + 1 + 2 + 3 = 12 \] Now, divide by the number of values (7): \[ \text{Mean Deviation} = \frac{12}{7} \approx 1.7143 \] ### Final Answer: The mean deviation of the first 7 natural numbers from their mean is approximately \(1.7143\).
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