Analysis on monthly incentive of 5 salesman shows the mean & median of the incentives is $7000. The mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest?

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Analysis on monthly incentive of 5 salesman shows the mean & median of the incentives is $7000. The mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest?

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Answer 1 · 2016-08-29T23:04:27

$$12,000 - $1,000 = $11,000$

Explanation:

Summarise the facts:

There are 5 salesmen and the mean of the incentives is 7,000
The median is 7,000 - in the middle
The mode is $12,000 rarr "at least 2 values of "12,000$

The first value we can calculate is the TOTAL amount (the sum of all the incentives)

$"TOTAL"/5 = 7,000$

$rArr TOTAL= 5xx7.000 = 35,000$

The middle value is 7000: So now, in order we have:

$............... ; .................; 7,000; .....................; ........................$

$12,000$ must occur exactly twice to be the mode..

$............... ; .................; 7,000; 12,000; 12,000.$

The remaining two values must add up to....

$35,000 - 7,000 - 2xx 12,000 =4,000$

They have to be full thousands: The amounts must be different otherwise there will be two modes, (So, it is not $2,000+2,000$ )

$1,000 + 3,000 = 4,000$

The five amounts are:

$1,000 ; 3,000 ; 7,000 ; 12,000 ; 12,000$

Highest - lowest = $12,000-1,000 = 11,000$

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Analysis on monthly incentive of 5 salesman shows the mean & median of the incentives is $7000. The mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest?

1 Answer

Explanation:

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