Help me plz? on a math question.?

Question

The CEO of a small buisness reports that the mean salary for the company's six employees is $67,000.00. If five of the six employees make less than 35,000.000, is this mean possible? Explain.

Plzz.. answer my question, and explain if its possible or not.
thanks!

Answer 1

It is certainly possible though the sixth employee will have a very large salary

(5*35000 +S)/6 = 67000
5*35000 +s = 6*67000
S =6* 67000 -5*35000
s=402000-175000
S = 227000
this is the 6 th salary if the others are making 35000 if they are making less the 6th salarty will be bigger try another example with each of the five salaries different.

(15000 +20000 +25000 +30000 +34000+ S)/6 =67000
(124000+S) =402000
S = 402000-124000 =278000

if you carry this to the extreme where the first five salaries are zero you find

(0+0+0+0+0+S)/6 = 67000
S= 402000
this is unlikely but still possible.

Answer 2

Yes, it is possible. If five employees were paid nothing at all, but the sixth were paid $402,000 (6 * $67,000), then the mean salary of the six employees would be $67,000.

When you have a group of data where individual values, or small numbers of values, are very different from most of the data, statisticians tend to use the median instead of the mean, because the mean can be misleading just as it is in your example.

Answer 3

Yeah, if the sixth employee made a lot more than 67, 000. if you assume the five made exactly 35,000 you could write an equation to figure out the sixth's salary:
(175,000+x) /6 = 67,000.

Answer 4

suppose x1, x2, x3, x4, x5 and x6 are the salaries of six employees. Then,

x1 + x2 +x3 +x4 +x5 + x6 / 6 = 67000

On the othert hand,

x1 + x2 + x3 + x4 + x5 / 5 < 35000

which means,

x1 + x2 + x3 + x4 + x5 < (5)(35000)
x1 + x2 + x3 + x4 + x5 < 175000

suppose x1 + x2 + x3 + x4 + x5 = 175000

Then, 175000 + x6 / 6 = 67000

x6 = 227000

So, the given mean salary of six employees is only possible when the sixth employee has more than 227000 salary.

Answer 5

Yes. mean is the average. if the mean (average) of 6 salaries is $67,000, that means that the total patroll is $67,000*6=$402,000.
lets say the 5 making <$35,000 make $30,000 each
$30,000*5=$150,000
$402,000-$15000=$252,000 for the salary of the 6th employee.

Answer 6

Yes. A sufficiently high sixth salary can make the mean be anything you want it to be.

Answer 7

outliers (in this case, a very large number, far from the median) can effect a mean, which in turn is why the median is often times prefered over the mean.

Answer 8

it's very simple (175,000+x) /6 = 67,000. the mean. see that wasn't so bad, just some easy algebra!