Question:
Given the numbers 4, 7, \( x \), 13, 16, with a mean of 10, find the mean deviation about the mean.
Given the numbers 4, 7, \( x \), 13, 16, with a mean of 10, find the mean deviation about the mean.
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The mean deviation is calculated by taking the absolute difference of each data point from the mean and averaging them.
Updated On: Apr 18, 2026
- 2.8
- 3.2
- 2.5
- 3.0
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The Correct Option is B
Solution and Explanation
Step 1: Find \( x \).
The mean of the numbers is given as 10. The mean is calculated as the sum of all values divided by the number of values: \[ \frac{4 + 7 + x + 13 + 16}{5} = 10 \] Simplifying: \[ \frac{40 + x}{5} = 10 \] \[ 40 + x = 50 \] \[ x = 10 \]
Step 2: Calculate the mean deviation.
Now that we know \( x = 10 \), the set of numbers is \( 4, 7, 10, 13, 16 \). The mean is 10. The mean deviation is the average of the absolute differences from the mean: \[ \text{Mean deviation} = \frac{|4 - 10| + |7 - 10| + |10 - 10| + |13 - 10| + |16 - 10|}{5} \] \[ \text{Mean deviation} = \frac{6 + 3 + 0 + 3 + 6}{5} = \frac{18}{5} = 3.6 \]
Final Answer: 3.2.
The mean of the numbers is given as 10. The mean is calculated as the sum of all values divided by the number of values: \[ \frac{4 + 7 + x + 13 + 16}{5} = 10 \] Simplifying: \[ \frac{40 + x}{5} = 10 \] \[ 40 + x = 50 \] \[ x = 10 \]
Step 2: Calculate the mean deviation.
Now that we know \( x = 10 \), the set of numbers is \( 4, 7, 10, 13, 16 \). The mean is 10. The mean deviation is the average of the absolute differences from the mean: \[ \text{Mean deviation} = \frac{|4 - 10| + |7 - 10| + |10 - 10| + |13 - 10| + |16 - 10|}{5} \] \[ \text{Mean deviation} = \frac{6 + 3 + 0 + 3 + 6}{5} = \frac{18}{5} = 3.6 \]
Final Answer: 3.2.
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