The following table shows the number of employees and their median age in eight companies located in a district. CompanyNumber of employeesMedian age A 32 24 B 28 30 C 43 39 D 39 45 E 35 49 F 29 54…
Question and options
The following table shows the number of employees and their median age in eight companies located in a district.
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
The median age of employees across the eight companies is:
| Company | Number of employees | Median age |
|---|---|---|
| A | 32 | 24 |
| B | 28 | 30 |
| C | 43 | 39 |
| D | 39 | 45 |
| E | 35 | 49 |
| F | 29 | 54 |
| G | 23 | 59 |
| H | 16 | 63 |
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
The median age of employees across the eight companies is:
- 45
- 54
- 49
- 47
Answer and explanation
Correct answer: A - 45
The overall median age is 45. There are 245 employees, so the median is the 123rd age, and the employees of A, B and C occupy the first 103 positions. The next 39 come from D, placing the overall median at D's 20th position, which is also D's median. Averaging the medians of D and E gives 47 because it treats companies as equally weighted observations.
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