What is the average age of the employees ?

Concept: The arithmetic mean (average) of a set of observations is the sum of all the observations divided by the number of observations: Mean = (Sum of all values) ÷ (Number of values). Each observation is counted exactly once, so no entry may be skipped or double-counted, and the resulting mean must always lie between the smallest and the largest observation in the set.

Application: The observations here are the 20 ages listed in the age column of the table, so n = 20. Adding them in blocks of five keeps the arithmetic short and easy to re-check.

1. Rows 1 to 5: 44 + 32 + 54 + 42 + 31 = 203.

2. Rows 6 to 10: 53 + 42 + 51 + 34 + 41 = 221, so the running total is 203 + 221 = 424.

3. Rows 11 to 15: 33 + 31 + 30 + 37 + 44 = 175, so the running total is 424 + 175 = 599.

4. Rows 16 to 20: 36 + 34 + 49 + 43 + 45 = 207, so the total of all 20 ages is 599 + 207 = 806 years.

5. Mean = Total ÷ n = 806 ÷ 20 = 40.3 years.

Cross-check (assumed-mean method): Take an assumed mean A = 40 and add only the deviations (age − 40): +4, −8, +14, +2, −9, +13, +2, +11, −6, +1, −7, −9, −10, −3, +4, −4, −6, +9, +3, +5. These deviations sum to +6, so Mean = A + (sum of deviations ÷ n) = 40 + 6 ÷ 20 = 40 + 0.3 = 40.3 years. An independent route gives the same value, which confirms the addition.

Result: The average age of the employees is 40.3 years. As a final sanity check, this lies inside the observed age range of 30 to 54 years, as any correct mean must, and close to the 30 to 49 year band where most of the listed ages sit.