In an office, mean of salaries of employees is ₹1,00,000 and median is ₹80,000. An employee will be considered, Grade A officer if his income is at least ₹85,000. Based on the above information check the validity of the following statements.

(i) Number of Grade A officers is more than or equal to number of non Grade A officers.

(ii) Mean of salaries of Grade A officers is more than ₹1,00,000.

Mean = ₹1,00,000

Median (mid value) = ₹80,000

This means:

50% employees earn ≤ ₹80,000

50% employees earn ≥ ₹80,000

(i) To be a Grade A officer, an employee must earn at least ₹85,000.

Since the income (₹85,000) is higher than the median (₹80,000), So fewer than 50% of the employees can qualify for Grade A.

∴ There will be more non Grade A officers than the Grade A officers.

Hence, statement (i) is false.

(ii) Given data shows that Mean (₹1,00,000) is significantly higher than the Median (₹80,000). This means there is a small group of very high earners pulling the average up.

The overall mean (₹1,00,000) includes non Grade A officers who earn less than ₹85,000. Therefore there group mean will definitely be below ₹85,000.

To pull this anchor of the non-Grade A officers up from less than ₹85,000 to a total average of ₹1,00,000, the Grade A officers must have a mean significantly higher than ₹1,00,000.

∴ Mean salaries of Grade A officers is more than ₹1,00,000.

Hence, statement (ii) is true.