What is the fraction of employees getting salary less than the average salary…

Concept — The average (arithmetic mean) of a set of values is their total divided by how many values there are: mean = (sum of all values) / (number of values). It is a single balancing figure for the whole set, expressed in the same unit as the values themselves.

A mean is not a positional measure: it need not split a data set into two equal halves — that is the median. A few unusually large values pull the mean upward, so more than half of the data can lie below it. The share of values lying below the mean therefore has to be counted, never assumed, and the required fraction is (number of values strictly less than the mean) / (total number of values).

Application — applying this to the 20 monthly salaries listed in the table:

1. Add all 20 salaries: 35 + 20 + 45 + 35 + 20 + 60 + 50 + 55 + 25 + 30 + 30 + 35 + 35 + 40 + 45 + 35 + 35 + 50 + 45 + 50 = 775 thousand rupees per month.

2. Divide the total by the number of employees: mean = 775 / 20 = 38.75 thousand rupees per month.

3. Count how many salaries are strictly less than 38.75 thousand. Grouping equal salaries first makes the count quick — the salary-wise tally is shown below.

4. Employees earning below the mean: 2 (at 20) + 1 (at 25) + 2 (at 30) + 6 (at 35) = 11 employees.

5. Turn that count into the fraction asked for: 11 / 20 = 0.55, that is 55 per cent of the employees.

Cross-check — the 9 employees at or above the mean earn 40, 45, 45, 45, 50, 50, 50, 55 and 60 thousand, and 11 + 9 = 20 accounts for every employee. The two salary totals reconcile as well: the 11 lower salaries add to 335 thousand and the 9 higher ones to 440 thousand, and 335 + 440 = 775 thousand, the total already used. The count sits above half because the handful of large salaries (55 and 60 thousand) lift the mean above the most common salary of 35 thousand, which alone is drawn by 6 of the 20 employees.

Result — 11 of the 20 employees draw less than the average salary of 38.75 thousand rupees per month, so the required fraction is 11/20 = 55 per cent.