Question

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?

Answer 1

`$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`