In 7 days, Mario cooked 98 pounds of spaghetti. Each day after the rst, he cooked 2 more pounds than he cooked than the day before. What is the difference between the average (arithmetic mean) number of pounds of spaghetti he cooked per day and the median number of pounds he cooked during 7 days ?

Answer 1

98/7 = 14 lbs/day average
7/2 (2a+6*2) = 98
so, a = 8

The median is the 4th day, so he cooked 8+3*2 = 14 lbs on that day.

So, the mean and median are the same. In fact, that is true for all arithmetic sequences.

Sn = n/2 (a1 + an) the mean is thus Sn/n = (a1+an)/2
The median is the n/2 term, which is a + (n-1)/2 * d = (2a + (n-1)d)/2 = (a1+an)/2