Explanation:

- The problem involves finding the mean of a set of values using deviations.

- The sum of deviations from 100 is -20. This means: (Sum of values) - 100n = -20.

- The sum of deviations from 92 is 140. This translates to: (Sum of values) - 92n = 140.

- Solving these:

- From the first equation: Sum of values = 100n - 20

- From the second equation: Sum of values = 92n + 140

- Equating the two:

- 100n - 20 = 92n + 140

- Rearranging gives: 8n = 160

- Solving for n gives: n = 20

- The mean µ is the Sum of values / n = (100n - 20) / n

- µ = (100 * 20 - 20) / 20

- µ = (2000 - 20) / 20

- µ = 1980 / 20

- µ = 99

- The correct answer is Option 4: 99.

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