Question

Need help with averages!!!!

Answer 1

The average (arithmetic mean) of a population in town x was recorded as 22,455 during the years 2000-2010. However, an error was later uncovered: the figure for 2009 was recorded as 22,478 when it should have been 22,500. What was the average population in town x during the years 2000-2010 once the error was corrected?

Answer 2

So they were 22 off.

Answer 3

mean = total number of people/total number of years

Answer 4

so how many years 2000 to 2010

Answer 5

you can simply find the "average of the extra 22" and add it to the given value

Answer 6

What? I just add it???

Answer 7

not quite

Answer 8

we'll use the arithmetic mean formula for the original numbers first

Answer 9

22455 = x/10 years

Answer 10

Oh!

Answer 11

x = 224550 people (note: this includes double-counted people)

Answer 12

then we add on the extra 22

Answer 13

and re-calculate the mean

Answer 14

Ok. Thanks @Vocaloid

Answer 15

or... if you are switched on to averages

22/11 = ? then the new average is 22455 + ?

Answer 16

22/11 = 2

Answer 17

Thanks @campbell_st I see.

Answer 18

there are 11 years between 2000 and 2010

both methods give the same answer. It just depends on how switched on you are with calculating the mean of a data set.

Answer 19

Thanks. That really does make sense. Thanks for helping me to think outside the box (at least in my mind!)