The sum of deviations of a set of n values measured from 50 is -10 and the sum of deviations of the values measured from 46 is 70. What is the mean of the values?
- A. 48.5
- B. 49.0
- C. 49.5 ✓
- D. 50.0
Correct Answer: C. 49.5
Explanation
Given \sum (x_i - 50) = -10 \implies \sum x_i - 50n = -10 and \sum (x_i - 46) = 70 \implies \sum x_i - 46n = 70. Subtracting the first from the second gives 4n = 80 \implies n = 20. Substitute n=20 back to find \sum x_i = 50(20) - 10 = 990. Mean = \frac{990}{20} = 49.5.
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