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The mean age can be calculated by adding up all the ages and then dividing by the total number of ages.
34 + 41 + 28 + 35 + 27 + 44 + 48 + 29 + 33 + 39 = 358
Dividing by 10 (the total number of ages) gives us: 358 / 10 = 35.8
Therefore, the mean age of the randomly selected employees is 35.8 years.