Classify the data of age of each employee in class interval of 5 years. Which…

Concept — Grouping into a class interval of 5 years means splitting the age range into non-overlapping 5-year classes such as 30-35, 35-40, 40-45, 45-50 and 50-55, and placing each value by the lower-limit-inclusive, upper-limit-exclusive rule, so an age of exactly 35 belongs to 35-40 and not to 30-35.

The average (arithmetic mean) of a class is the sum of the values falling in that class divided by the number of members of that class, mean = (sum of salaries) / (number of employees). Because a mean is a ratio and not a total, the class with the biggest salary bill need not have the biggest average: a small class of highly paid members can outrank a large class.

Application — applying this to the 20 employees in the table:

1. Form the 5-year age classes the data spans: 30-35, 35-40, 40-45, 45-50 and 50-55.

2. Place every employee in a class by age: 30-35 takes the ages 30, 31, 31, 32, 33, 34 and 34; 35-40 takes 36 and 37; 40-45 takes 41, 42, 42, 43, 44 and 44; 45-50 takes 45 and 49; 50-55 takes 51, 53 and 54.

3. Add the salaries inside each class, count the members of that class, and divide the total by the count.

Cross-check — the 40-45 class carries the largest salary bill of the five, 240 thousand, yet its average is only 40 thousand because that bill is spread over 6 employees; the question asks for the mean, not the total. The result is also stable under the opposite boundary convention: if the 45-year-old earning 50 thousand were counted in 40-45 instead, that class would average 290/7 = 41.43 and 45-50 would average 50, while 50-55 is untouched at 160/3 = 53.33.

Result — the 50 - 55 year class has the maximum average salary, about 53.33 thousand rupees per month.