What is the new average and median salary of people on the bus?

Question

9 people on a bus in Seattle and the average of their yearly income is $65,000. At the next stop, the highest paid person on the bus (with an income of $120,000 per year) gets off and Bill Gates gets on. Mr. Gates makes 7.6 Billion dollars a year. What is the new average and median salary of people on the bus?

Answer 1

The median of a set of numbers is the number in the middle when you list them in order. For example, the median of {1, 2, 4, 7, 15} is 4. If you replace the highest number with a different number, the median will not change. In this example, {1, 2, 4, 7, 500} still has a median of 4.

 

Average salary is the total salary of a group divided by the number of people. We know the guy who left had 120,000/yr salary, the original average is 65,000/yr, and there were 9 people. You can use this to find the total salary S of the other 8 people.

(120,000 + S)/9 = 65,000

You can solve this for S fairly readily.

 

Now you can calculate the new average with Bill Gates' salary in place of the 120,000.

 

(7,600,000,000 + S)/9 = new average