The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

1 Answer
Sep 8, 2016

Average (arithmetic mean) of the integers from #200# to #400#, inclusive, is greater than the average of the integers from #50# to #100# by #225#.

Explanation:

Number of integers from #200# to #400# is #400-199=201#

As it forms an arithmetic series starting from #200# and common difference #1#, sum of series is

#201/2(2xx200+(201-1)xx1)=201/2xx(400+200)#

= #201xx300=60300#

and hence average is #60300/201=300#

Number of integers from #50# to #100# is #100-49=51#

As it forms an arithmetic series starting from #50# and common difference #1#, sum of series is

#51/2(2xx50+(51-1)xx1)=51/2xx(100+50)#

= #51xx75=3825#

and hence average is #3825/51=75# and

Average (arithmetic mean) of the integers from #200# to #400#, inclusive, is greater than the average of the integers from #50# to #100# by #300-75=225#.