A small town has an adult population of 100. One person is a multi-millionaire who make $5,000,000 per year. The mean annual salary in the town is $74,750. Is the mean a fair measure of a typical salary in the town? What is the mean annual salary of the other 99 adults?
please answer and show work
thanks
2007-01-08 13:39:42 · 9 answers · asked by NABEELiOS 1 in Science & Mathematics ➔ Mathematics
Probably not.
Let x be the average salary of everyone else. Then 99x is the total amount that all 99 of them earn in a year.
Using the formula for the average:
(99x + 5,000,000)/100 = 74,750
Multiply both sides by 100:
99x + 5,000,000 = 7,475,000
Subtract the multimillionaire's salary:
99x = 2,475,000
Then the remaining 99 people earn a total of $2,475,000, so each earns, on average:
x = $25,000
The average salary of everyone else is only $25,000, so the multi-millionaire's salary inflates the average salary by almost three times.
2007-01-08 13:43:43 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
Mean is Average. The mean annual salary of the town of 100 is $74,750. So the total annual salary of the town if $74,750 x 100 = $$7,475,000.
If one Multi-millionaire makes $5,000,000 per year, the rest of the 99 adults would be earning $(7,475,000 - 5,000,000) = $2,475,000.
So the mean of the other 99 adults would be $(2,475,000 / 99) = $25,000.
In this case, the mean is not a fair measure because of the multi-millionair's income of $5m.
2007-01-08 14:19:29 · answer #2 · answered by vach1970 2 · 0⤊ 0⤋
Hi I'm no maths whiz but this is what I came up with.
MEAN is the average scores right. so, $74,750 is all the salaries including the millionaire.
$74,750 x 100 = $7,475,000 - $5,000,000 = $2,475,000
$2,475,000 divide by 99 = $25,000
the other 99 would average $25,000 per year.
if you go back to the mean annual salary answer of $74,750 it will come out right ie
$25,000 x 99 = $2,475,000 + $5,000,000 (millionaire) = $7,475,000 which then you have to divide by 100 = $74,750 to get the mean.
So in answer to the question: NO the mean is not a fair measure of the typical salary in the town. The other 99 adults earn $25,000 per year.
Good luck.
2007-01-08 14:06:35 · answer #3 · answered by Mrssunshine 2 · 0⤊ 0⤋
74,750 x 100
7,475,000
Discount the 5 million.
2,475,000
100 people
Discount the millionaire.
100 - 1 = 99
2,475,000 $ Divided by 99 = about 24,250.00 $
2007-01-08 13:47:07 · answer #4 · answered by Anonymous · 0⤊ 0⤋
One outlier throws the mean way off, and makes the median a better indicator of average.
Here, if x is the other 99 peoples' mean,
(99x + 5,000,000)/100 = 74, 750
mult both by 100
99x + 5000000 = 7475000
subtract, divide,... you know the rest
2007-01-08 13:45:55 · answer #5 · answered by hayharbr 7 · 0⤊ 0⤋
(99x+5,000,000)/100=$74,750
99x+5,000,000 = 7,475,000
99x = 2,475,000
x = $25,000
2007-01-08 13:45:01 · answer #6 · answered by aficionado210 2 · 0⤊ 0⤋
about 35,000 a year.
2007-01-08 13:42:53 · answer #7 · answered by DXL 1 · 0⤊ 1⤋
sorry kiddo- do your own homework
2007-01-08 13:47:01 · answer #8 · answered by Mopar Muscle Gal 7 · 1⤊ 1⤋
80,000
2007-01-08 13:42:25 · answer #9 · answered by Anonymous · 0⤊ 1⤋