There are 10 employees in an office. The table shows how many employees have 0, 1, 2 or 3 pets. If the office manager were included in the table, the average (arithmetic mean) number of pets per person would equal the median number of pets per person. How many pets does the office manager have?
Table:
# of pets------# of employees
0------------------2
1------------------3
2------------------2
3------------------3
Answer choices:
3
4
5
6
7
Total number of pets = (number of employees)(average number of pets per employee).
Since the average is equal to the median, we get:
Total number of pets = (number of employees)(median number of pets per employee).
Pet values:
2 employees each have 0 pets --> 0, 0
3 employees each have 1 pet --> 1, 1, 1
2 employees each have 2 pets --> 2, 2
3 employees each have 3 pets --> 3, 3, 3
Manager has x pets --> x.
Since the answer choices are all 3 or greater, the manager must have at least 3 pets.
Listing the pet values in order, we get:
0, 0, 1, 1, 1,
2, 2, 3, 3, 3, x
Since there are 11 employees, and the median number of pets is 2, we get:
Total number of pets = 11*2 = 22.
Thus:
0+0+1+1+1+2+2+3+3+3+x = 22
16+x = 22
x = 6.
The correct answer is
D.
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